Question : Directions: Three Statements are given followed by three conclusions numbered I, II and III. 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:
I. Some sweets are chocolates.
II. All chocolates are cookies.
III. Some cookies are healthy.
Conclusions:
I. Some sweets are cookies.
II. Some cookies are chocolates.
III. Some chocolates are sweets.
Option 1: Both conclusions II and III follow
Option 2: Both conclusions I and III follow
Option 3: Both conclusions I and II follow
Option 4: All conclusions follow
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Correct Answer: All conclusions follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some sweets are cookies – From the Venn diagram, it is clear that the circle of sweets and cookies intersect and have some common area between them. Therefore, this conclusion follows.
Conclusion (II):
Some cookies are chocolates – From the Venn diagram, it is clear that some part of the cookies lies inside the circle of chocolates and some lie outside. Therefore, this conclusion follows.
Conclusion (III):
Some chocolates are sweets – From the Venn diagram, it is clear that the circle of sweets and chocolates intersect and have some common area between them. Therefore, this conclusion follows.
Therefore, all conclusions follow. Hence, the fourth option is correct.
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