ISI TOMATO book

Question

P, Q and R are statements such that if P is true then at least one
of the following is correct : (i) Q is true, (ii) R is not true. Then
(a) if both P and Q are true then R is true
(b) if both Q and R are true then P is true
(c) if both P and R are true then Q is true
(d) none of the foregoing statements is correct.

 

Here the given answer is c but options a & b also make the given condition true i.e. either of the two statements is correct.For option a) P is true and Q is true then R is true is given statement which makes condition 1 true and condition 2 false which also holds.

Kindly Explain

Comments

Convert the given statement in the question:-

$(P\leftarrow\rightarrow T) \rightarrow ((Q \leftarrow\rightarrow T)\vee(R \leftarrow\rightarrow F))$

Converting option (C) into Logic :-

$(P \wedge R) \rightarrow Q$

if both P and R are True and Q is true then above statement is true.

if both P and R are True and Q is false then above statement is false.

which means it is satisfying the above constraint. Hence it should be answer.