### Brain Teasers

# Who Likes Whom ?

The relationships of a person X with 3 people P, Q and R are given below.

1) X likes at least one of the three people.

2) If X likes P, but not R, then he also likes Q.

3) X likes both R and Q, or he likes neither of them.

4) If X likes R, then he also likes P.

Which of the following statements can be deduced from the above?

A) X likes P, Q and R.

B) X likes only P.

C) X likes only Q.

D) X likes P and Q only.

NOTE: Out of the given set of 4 statements, it is not necessary that one and only one statement can be deduced. One or more statements may be possible to be deduced.

1) X likes at least one of the three people.

2) If X likes P, but not R, then he also likes Q.

3) X likes both R and Q, or he likes neither of them.

4) If X likes R, then he also likes P.

Which of the following statements can be deduced from the above?

A) X likes P, Q and R.

B) X likes only P.

C) X likes only Q.

D) X likes P and Q only.

NOTE: Out of the given set of 4 statements, it is not necessary that one and only one statement can be deduced. One or more statements may be possible to be deduced.

### Answer

Only statement A which states that X likes P, Q and R can be deduced.The relationships given are

1) X likes at least one of the three people.

2) If X likes P, but not R, then he also likes Q.

3) X likes both R and Q, or he likes neither of them.

4) If X likes R, then he also likes P.

The statements given are

A) X likes P, Q and R.

B) X likes only P.

C) X likes only Q.

D) X likes P and Q only.

From relationship 3, we can get the following two cases:-

Case 1 : Let us assume that X neither likes R nor Q. It implies that he likes P since from relationship 1, he likes at least one of the three. However relationship 2 which says that if X likes P, but not R, then X also likes Q contradicts the above observation.

Case 2 : Let us assume that X likes both R and Q. Then from relationship 4, X likes P also, since he likes R. This does not violate any of the given relationships.

Since we know that only the above two cases are possible and Case 1 being ruled out due to contradictory statements, from observation 2 we can deduce only statement A which says that X likes P, Q and R.

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