Syllogisms

Solution

Statements: No ropes are hills. Some ropes are plates. Combining them in a Venn diagram, these must be true: Some ropes are not hills. Some plates are not hills. I: 'No ropes are plates' does not follow. A diagram with items that are hills but not ropes or plates; items that are ropes and plates but not hills satisfies all statements but makes it false. II: 'Some ropes are not hills' follows. Answer: Only conclusion II follows

Solution

Statements: No doors are birds. Some birds are stones. Combining them in a Venn diagram, these must be true: Some birds are not doors. Some stones are not doors. I: 'Some birds are not doors' follows. II: 'Some stones are not doors' follows. Answer: Both conclusions I and II follow

Solution

Statements: All windows are roads. Some keys are windows. Combining them in a Venn diagram, these must be true: Some roads are windows. Some roads are keys. I: 'Some roads are windows' follows. II: 'Some keys are not windows' does not follow. A diagram with items that are roads and windows and keys satisfies all statements but makes it false. Answer: Only conclusion I follows

Solution

Statements: No bags are hills. No hills are lamps. Combining them in a Venn diagram gives no new definite relation. I: 'All hills are bags' does not follow. A diagram with items that are hills but not bags or lamps; items that are bags and lamps but not hills satisfies all statements but makes it false. II: 'No lamps are bags' does not follow. A diagram with items that are hills but not bags or lamps; items that are bags and lamps but not hills satisfies all statements but makes it false. Answer: Neither conclusion I nor II follows

Solution

Statements: Some drums are hills. No hills are cars. Combining them in a Venn diagram, these must be true: Some drums are not cars. Some hills are not cars. I: 'Some hills are cars' does not follow. A diagram with items that are drums and hills but not cars; items that are cars but not drums or hills satisfies all statements but makes it false. II: 'Some drums are not cars' follows. Answer: Only conclusion II follows

Solution

Statements: Some apples are doors. No apples are plates. Combining them in a Venn diagram, these must be true: Some doors are not plates. Some apples are not plates. I: 'All apples are plates' does not follow. A diagram with items that are doors and apples but not plates; items that are plates but not doors or apples satisfies all statements but makes it false. II: 'Some plates are not doors' does not follow. A diagram with items that are doors and apples but not plates; items that are doors and plates but not apples satisfies all statements but makes it false. Answer: Neither conclusion I nor II follows

Solution

Statements: Some roads are clocks. No clocks are lamps. Combining them in a Venn diagram, these must be true: Some roads are not lamps. Some clocks are not lamps. I: 'Some clocks are not lamps' follows. II: 'All roads are lamps' does not follow. A diagram with items that are roads and clocks but not lamps; items that are lamps but not roads or clocks satisfies all statements but makes it false. Answer: Only conclusion I follows

Solution

Statements: All ships are rivers. No flowers are rivers. Combining them in a Venn diagram, these must be true: No ships are flowers. I: 'Some rivers are not ships' does not follow. A diagram with items that are ships and rivers but not flowers; items that are flowers but not ships or rivers satisfies all statements but makes it false. II: 'No flowers are ships' follows. Answer: Only conclusion II follows

Solution

Statements: All flowers are keys. Some drums are flowers. Combining them in a Venn diagram, these must be true: Some keys are flowers. Some keys are drums. I: 'Some keys are flowers' follows. II: 'Some keys are drums' follows. Answer: Both conclusions I and II follow

Solution

Statements: No kites are chairs. Some boxes are chairs. Combining them in a Venn diagram, these must be true: Some chairs are not kites. Some boxes are not kites. I: 'Some boxes are not kites' follows. II: 'Some chairs are not kites' follows. Answer: Both conclusions I and II follow

Solution

Statements: Some doors are rivers. All doors are shirts. Combining them in a Venn diagram, these must be true: Some rivers are shirts. Some doors are shirts. I: 'Some doors are shirts' follows. II: 'No shirts are rivers' does not follow. A diagram with items that are rivers and doors and shirts satisfies all statements but makes it false. Answer: Only conclusion I follows

Solution

Statements: No shirts are tables. Some tables are roads. Combining them in a Venn diagram, these must be true: Some tables are not shirts. Some roads are not shirts. I: 'Some roads are not shirts' follows. II: 'All tables are shirts' does not follow. A diagram with items that are shirts but not tables or roads; items that are tables and roads but not shirts satisfies all statements but makes it false. Answer: Only conclusion I follows

Solution

Statements: No birds are chairs. Some gloves are chairs. Combining them in a Venn diagram, these must be true: Some chairs are not birds. Some gloves are not birds. I: 'All chairs are gloves' does not follow. A diagram with items that are birds but not chairs or gloves; items that are chairs but not birds or gloves; items that are chairs and gloves but not birds satisfies all statements but makes it false. II: 'Some gloves are not birds' follows. Answer: Only conclusion II follows

Solution

Statements: No cars are clocks. Some cars are roads. Combining them in a Venn diagram, these must be true: Some cars are not clocks. Some roads are not clocks. I: 'All roads are cars' does not follow. A diagram with items that are clocks and roads but not cars; items that are cars and roads but not clocks satisfies all statements but makes it false. II: 'Some cars are clocks' does not follow. A diagram with items that are clocks but not cars or roads; items that are cars and roads but not clocks satisfies all statements but makes it false. Answer: Neither conclusion I nor II follows

Solution

Statements: Some shoes are bags. No shoes are ships. Combining them in a Venn diagram, these must be true: Some bags are not ships. Some shoes are not ships. I: 'Some shoes are not ships' follows. II: 'Some bags are not ships' follows. Answer: Both conclusions I and II follow

Solution

Statements: All tables are trees. No trees are rivers. Combining them in a Venn diagram, these must be true: No tables are rivers. 'No tables are rivers' follows from these. 'Some tables are rivers' does not follow: a diagram with items that are tables and trees but not rivers; items that are rivers but not tables or trees satisfies the statements but makes it false. 'All rivers are trees' does not follow: a diagram with items that are tables and trees but not rivers; items that are rivers but not tables or trees satisfies the statements but makes it false. Answer: No tables are rivers

Solution

Statements: All trees are books. Some coins are not books. Combining them in a Venn diagram, these must be true: Some coins are not trees. 'Some coins are not trees' follows from these. 'All coins are books' does not follow: a diagram with items that are trees and books but not coins; items that are coins but not trees or books satisfies the statements but makes it false. 'All coins are trees' does not follow: a diagram with items that are trees and books but not coins; items that are coins but not trees or books satisfies the statements but makes it false. Answer: Some coins are not trees

Solution

Statements: Some ropes are pens. No pens are clouds. Combining them in a Venn diagram, these must be true: Some ropes are not clouds. Some pens are not clouds. 'Some ropes are not clouds' follows from these. 'Some ropes are clouds' does not follow: a diagram with items that are ropes and pens but not clouds; items that are clouds but not ropes or pens satisfies the statements but makes it false. 'All pens are ropes' does not follow: a diagram with items that are pens but not ropes or clouds; items that are ropes and pens but not clouds; items that are clouds but not ropes or pens satisfies the statements but makes it false. Answer: Some ropes are not clouds

Solution

Statements: No plates are birds. Some plates are gloves. Combining them in a Venn diagram, these must be true: Some plates are not birds. Some gloves are not birds. 'Some plates are not birds' follows from these. 'All gloves are birds' does not follow: a diagram with items that are birds but not plates or gloves; items that are plates and gloves but not birds satisfies the statements but makes it false. 'Some birds are plates' does not follow: a diagram with items that are birds but not plates or gloves; items that are plates and gloves but not birds satisfies the statements but makes it false. Answer: Some plates are not birds

Solution

Statements: Some hills are shirts. No coins are shirts. Combining them in a Venn diagram, these must be true: Some hills are not coins. Some shirts are not coins. 'Some shirts are not coins' follows from these. 'All hills are coins' does not follow: a diagram with items that are hills and shirts but not coins; items that are coins but not hills or shirts satisfies the statements but makes it false. 'All hills are shirts' does not follow: a diagram with items that are hills and shirts but not coins; items that are hills and coins but not shirts satisfies the statements but makes it false. Answer: Some shirts are not coins

Solution

Statements: All coins are clouds. All lamps are coins. Combining them in a Venn diagram, these must be true: All lamps are clouds. 'All lamps are clouds' follows from these. 'No clouds are lamps' does not follow: a diagram with items that are clouds and coins and lamps satisfies the statements but makes it false. 'All clouds are coins' does not follow: a diagram with items that are clouds but not coins or lamps; items that are clouds and coins and lamps satisfies the statements but makes it false. Answer: All lamps are clouds

Solution

Statements: All drums are rivers. Some bags are not rivers. Combining them in a Venn diagram, these must be true: Some bags are not drums. 'Some bags are not drums' follows from these. 'All rivers are bags' does not follow: a diagram with items that are drums and rivers but not bags; items that are bags but not drums or rivers satisfies the statements but makes it false. 'All bags are rivers' does not follow: a diagram with items that are drums and rivers but not bags; items that are bags but not drums or rivers satisfies the statements but makes it false. Answer: Some bags are not drums

Solution

Statements: All cars are rivers. All rivers are bricks. Combining them in a Venn diagram, these must be true: All cars are bricks. 'All cars are bricks' follows from these. 'No cars are bricks' does not follow: a diagram with items that are cars and rivers and bricks satisfies the statements but makes it false. 'No cars are rivers' does not follow: a diagram with items that are cars and rivers and bricks satisfies the statements but makes it false. Answer: All cars are bricks

Solution

Statements: All cars are stones. Some ropes are cars. Combining them in a Venn diagram, these must be true: Some stones are cars. Some stones are ropes. 'Some stones are ropes' follows from these. 'Some ropes are not stones' does not follow: a diagram with items that are stones and cars and ropes satisfies the statements but makes it false. 'Some cars are not stones' does not follow: a diagram with items that are stones and cars and ropes satisfies the statements but makes it false. Answer: Some stones are ropes

Solution

Statements: All apples are ships. No ships are doors. Combining them in a Venn diagram, these must be true: No apples are doors. 'No apples are doors' follows from these. 'Some apples are doors' does not follow: a diagram with items that are apples and ships but not doors; items that are doors but not apples or ships satisfies the statements but makes it false. 'All doors are ships' does not follow: a diagram with items that are apples and ships but not doors; items that are doors but not apples or ships satisfies the statements but makes it false. Answer: No apples are doors

Solution

Statements: All bottles are cars. Some bottles are shoes. Combining them in a Venn diagram, these must be true: Some cars are bottles. Some cars are shoes. 'Some cars are shoes' follows from these. 'All cars are bottles' does not follow: a diagram with items that are cars but not bottles or shoes; items that are cars and bottles and shoes satisfies the statements but makes it false. 'All cars are shoes' does not follow: a diagram with items that are cars but not bottles or shoes; items that are cars and bottles and shoes satisfies the statements but makes it false. Answer: Some cars are shoes

Solution

Statements: No windows are keys. All tables are windows. Combining them in a Venn diagram, these must be true: No keys are tables. 'No keys are tables' follows from these. 'No windows are tables' does not follow: a diagram with items that are keys but not windows or tables; items that are windows and tables but not keys satisfies the statements but makes it false. 'Some windows are not tables' does not follow: a diagram with items that are keys but not windows or tables; items that are windows and tables but not keys satisfies the statements but makes it false. Answer: No keys are tables

Solution

Statements: All hills are lamps. All lamps are bottles. Combining them in a Venn diagram, these must be true: All hills are bottles. 'All hills are bottles' follows from these. 'Some lamps are not bottles' does not follow: a diagram with items that are hills and lamps and bottles satisfies the statements but makes it false. 'Some hills are not lamps' does not follow: a diagram with items that are hills and lamps and bottles satisfies the statements but makes it false. Answer: All hills are bottles

Solution

Statements: Some ropes are keys. All ropes are bricks. Combining them in a Venn diagram, these must be true: Some keys are bricks. Some ropes are bricks. 'Some keys are bricks' follows from these. 'Some ropes are not bricks' does not follow: a diagram with items that are keys and ropes and bricks satisfies the statements but makes it false. 'No keys are bricks' does not follow: a diagram with items that are keys and ropes and bricks satisfies the statements but makes it false. Answer: Some keys are bricks

Solution

Statements: Some rivers are stones. No trees are rivers. Combining them in a Venn diagram, these must be true: Some stones are not trees. Some rivers are not trees. 'Some stones are not trees' follows from these. 'All stones are trees' does not follow: a diagram with items that are stones and rivers but not trees; items that are trees but not stones or rivers satisfies the statements but makes it false. 'All rivers are trees' does not follow: a diagram with items that are stones and rivers but not trees; items that are trees but not stones or rivers satisfies the statements but makes it false. Answer: Some stones are not trees

Solution

Statements: Some lamps are not doors. All lamps are clocks. Combining them in a Venn diagram, these must be true: Some lamps are clocks. Some clocks are not doors. 'Some clocks are not doors' follows from these. 'No lamps are clocks' does not follow: a diagram with items that are doors but not lamps or clocks; items that are lamps and clocks but not doors satisfies the statements but makes it false. 'All doors are lamps' does not follow: a diagram with items that are doors but not lamps or clocks; items that are lamps and clocks but not doors satisfies the statements but makes it false. Answer: Some clocks are not doors

Solution

Statements: All mirrors are books. Some flowers are mirrors. Combining them in a Venn diagram, these must be true: Some books are mirrors. Some books are flowers. 'Some books are flowers' follows from these. 'Some mirrors are not books' does not follow: a diagram with items that are books and mirrors and flowers satisfies the statements but makes it false. 'No books are flowers' does not follow: a diagram with items that are books and mirrors and flowers satisfies the statements but makes it false. Answer: Some books are flowers

Solution

Statements: Some bottles are apples. All bottles are windows. Combining them in a Venn diagram, these must be true: Some apples are windows. Some bottles are windows. 'Some bottles are windows' follows from these. 'All bottles are apples' does not follow: a diagram with items that are bottles and windows but not apples; items that are apples and bottles and windows satisfies the statements but makes it false. 'All windows are apples' does not follow: a diagram with items that are windows but not apples or bottles; items that are apples and bottles and windows satisfies the statements but makes it false. Answer: Some bottles are windows

Solution

Statements: Some shoes are not windows. No shoes are lamps. Combining them in a Venn diagram, these must be true: Some shoes are not lamps. 'Some shoes are not lamps' follows from these. 'Some lamps are not windows' does not follow: a diagram with items that are shoes but not windows or lamps; items that are windows and lamps but not shoes satisfies the statements but makes it false. 'All lamps are shoes' does not follow: a diagram with items that are shoes but not windows or lamps; items that are windows and lamps but not shoes satisfies the statements but makes it false. Answer: Some shoes are not lamps

Solution

Statements: No cars are bricks. Some bricks are not bottles. Combining them in a Venn diagram, these must be true: Some bricks are not cars. 'Some bricks are not cars' follows from these. 'All bottles are bricks' does not follow: a diagram with items that are bricks but not cars or bottles; items that are cars and bottles but not bricks satisfies the statements but makes it false. 'All cars are bottles' does not follow: a diagram with items that are cars but not bricks or bottles; items that are bricks but not cars or bottles; items that are bottles but not cars or bricks satisfies the statements but makes it false. Answer: Some bricks are not cars

Solution

Statements: All windows are cars. Some windows are not ropes. All clouds are ropes. Combining them in a Venn diagram, these must be true: Some cars are windows. Some cars are not ropes. Some cars are not clouds. Some windows are not clouds. I: 'Some cars are not windows' does not follow. A diagram with items that are cars and windows but not ropes or clouds; items that are ropes and clouds but not cars or windows satisfies all statements but makes it false. II: 'Some cars are not ropes' follows. Answer: Only conclusion II follows

Solution

Statements: No keys are rivers. Some clocks are rivers. All clocks are stones. Combining them in a Venn diagram, these must be true: Some rivers are stones. Some clocks are stones. Some rivers are not keys. Some clocks are not keys. I: 'Some stones are rivers' follows. II: 'Some stones are not keys' follows. Answer: Both conclusions I and II follow

Solution

Statements: Some gloves are not roads. All gloves are drums. Some ropes are not drums. Combining them in a Venn diagram, these must be true: Some gloves are drums. Some drums are not roads. Some ropes are not gloves. I: 'Some gloves are drums' follows. II: 'Some ropes are not gloves' follows. Answer: Both conclusions I and II follow

Solution

Statements: Some windows are not doors. Some hills are windows. Some coins are hills. Combining them in a Venn diagram gives no new definite relation. I: 'Some coins are not hills' does not follow. A diagram with items that are windows and hills but not doors or coins; items that are doors and hills and coins but not windows satisfies all statements but makes it false. II: 'Some hills are doors' does not follow. A diagram with items that are doors but not windows or hills or coins; items that are windows and hills and coins but not doors satisfies all statements but makes it false. Answer: Neither conclusion I nor II follows

Solution

Statements: All drums are clocks. No clocks are gloves. Some gloves are kites. Combining them in a Venn diagram, these must be true: No drums are gloves. Some gloves are not drums. Some gloves are not clocks. Some kites are not drums. I: 'Some gloves are drums' does not follow. A diagram with items that are drums and clocks but not gloves or kites; items that are gloves and kites but not drums or clocks satisfies all statements but makes it false. II: 'Some gloves are not clocks' follows. Answer: Only conclusion II follows

Solution

Statements: Some doors are stones. All doors are windows. Some books are not windows. Combining them in a Venn diagram, these must be true: Some stones are windows. Some doors are windows. Some books are not doors. I: 'Some doors are windows' follows. II: 'Some stones are windows' follows. Answer: Both conclusions I and II follow

Solution

Statements: Some mirrors are clocks. Some mirrors are trees. All trees are tables. Combining them in a Venn diagram, these must be true: Some mirrors are tables. Some trees are tables. I: 'Some tables are mirrors' follows. II: 'Some trees are clocks' does not follow. A diagram with items that are clocks and mirrors but not trees or tables; items that are mirrors and trees and tables but not clocks satisfies all statements but makes it false. Answer: Only conclusion I follows

Solution

Statements: No bags are coins. All bags are bottles. All bottles are windows. Combining them in a Venn diagram, these must be true: All bags are windows. I: 'All bags are windows' follows. II: 'No windows are bottles' does not follow. A diagram with items that are coins but not bags or bottles or windows; items that are bags and bottles and windows but not coins satisfies all statements but makes it false. Answer: Only conclusion I follows

Solution

Statements: All kites are doors. Some buses are kites. Some buses are chairs. Combining them in a Venn diagram, these must be true: Some doors are kites. Some doors are buses. I: 'Some doors are not buses' does not follow. A diagram with items that are doors and kites and buses but not chairs; items that are buses and chairs but not doors or kites satisfies all statements but makes it false. II: 'Some kites are doors' follows. Answer: Only conclusion II follows

Solution

Statements: Some chairs are bags. No bags are plates. Some plates are not boxes. Combining them in a Venn diagram, these must be true: Some chairs are not plates. Some bags are not plates. Some plates are not bags. I: 'All bags are boxes' does not follow. A diagram with items that are chairs and bags but not plates or boxes; items that are plates but not chairs or bags or boxes; items that are boxes but not chairs or bags or plates satisfies all statements but makes it false. II: 'All boxes are plates' does not follow. A diagram with items that are plates but not chairs or bags or boxes; items that are chairs and bags and boxes but not plates satisfies all statements but makes it false. Answer: Neither conclusion I nor II follows