Question : Directions: Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All bats are sticks.
No stick is a ball.
Conclusions:
I. No bat is a ball.
II. No ball is a bat.
Option 1: Neither conclusion I nor II follows
Option 2: Only conclusion I follows
Option 3: Only conclusion II follows
Option 4: Both conclusions I and II follow
Correct Answer: Both conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
No bat is a ball – From the given Venn diagram, the circle of the bat is completely inside the circle of the stick, and as per the given statements no stick is a ball. Therefore, this conclusion is true.
Conclusion (II):
No ball is a bat – From the given Venn diagram, the circle of the bat is completely inside the circle of the stick, and as per the given statements no stick is a ball. Therefore, this conclusion is true.
So, both conclusions I and II follow. Hence, the fourth option is correct.
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