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Syllogisms: Quick Solving Tips By Bhagyashree Ghosh

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Solving Syllogism through Venn Diagram 13

e Solving Syllogism usingq_Venn diagram Venn diagram method is an effective and precise method to solve syllogism problems. Steps to solve: In order to solve a syllogism, first draw the standard diagram based on the given statements. D Then try to check which of the given conclusions follow irn every possible case. O If a conclusion is true for one case but is negated for the other possible representation, it is not considered as a conclusion In other words, a conclusion follows only if it is true for all the possible cases

Example 1: Statements: Some reds are crows. All crows are yellows. All yellows are rabbits. Conclusions 1. All crows are rabbits. Il. Some yellows are reds. Ill. Some reds are rabbits. Solution: From the first statement, some reds are crows. This can be represented as

O From the first statement, some reds are crows. This can be represented as: Red Crow O Next we have all crows are yellows. So the circle yellow' must engulf 'crow' Re Crow Yellow

O Next we have all yellows are rabbits. So the circle 'rabbit' engulfs 'yellow' Re Crow Rabbit This is the standard representation of all the statements taken together. Now we shall check the conclusions based on this representation.

Conclusion l: All crows are rabbits From the diagram, we can see that the circle 'rabbit' engulfs the circle 'crow'. So conclusion I follows. Conclusion Il: Some yellows are reds We can see that the circles 'yellow' and 'red' intersect each other. So conclusion Il also follows. Conclusion III: Some reds are rabbits We can see that the circles 'rabbit' and 'red' intersect each other. So conclusion IlI also follows. Hence all of the given conclusions follow.

e Example 2: Statements: All cars are bikes, Some bikes are ships, All ships are planes Conclusions: I. At least some planes are bikes. ll. Some bikes are cars. II. All planes are cars is a possibility Solution: From the first statement, the standard diagram can be drawn as follows.

Ship From this, we can say that conclusions l and 11 follow, but does not. But we can have another representation of the given statements as below: Hence all conclusions follows Ship Plane ar Bike