Whichever book Mr A reads Mr B also reads that book Whichever book Mr B reads Mrs C also reads that ...........

Logical Reasonong (PCS) Statement - Conclusions

Whichever book Mr. A reads, Mr. B also reads that book. Whichever book Mr. B reads, Mrs. C also reads that book. Which of the following must be true ?

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PCS Previous year General Studies paper (2018)

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Mr. B has not read the Shiva trilogy. So Mrs. C could not have read it.

Mr. B has read the Harry Potter series. So Mr. A must have read it.

Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.

Mrs. C has read all the books written by Paulo Coelho. Mr. A must have read all of those as well.

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Explanation:

Correct option 3: Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.

Given:

If Mr. A reads a book, then Mr. B reads it. (A ? B)
If Mr. B reads a book, then Mrs. C reads it. (B ? C)

This gives us a chain:
A ? B ? C, or equivalently A ? C

Option 3:
Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.

Let's test it logically:

If Mrs. C has NOT read the book ⇒ Then Mr. B did not read it (by contrapositive of B ? C),
and if Mr. B did NOT read it, then Mr. A could NOT have read it (by contrapositive of A ? B)

So this does logically follow by contrapositive: