Hi Manisha,

We are given that if both P and Q are true, then R is false; and if P is false, then S is false. Given that R is true, it follows that both P and Q are not true.

Now, let's consider the options:

(A) If R is true, then P can be false, Q can be false, or both P and Q can be false. Therefore, there are cases where Q can be true as well, so this statement is not always true.

(B) If S is false, then P can be true or false, and the implication is not bidirectional. Even if P were true, S can still be false. Hence, there are no additional restrictions compared to option A; P can be both true or false.

(C) If S is true, then P is definitely true, because if P were false, S would have been false. Given S is true, P is true, and R is false. If both P and Q were true, R would have been false, meaning one of P or Q is false. Since P is true, Q must be false. This option states that Q is true, so we can eliminate it.

(D) Using the logic from option C, if S is true, then Q must be false. This makes option D our answer.
Hope this helps!
Please feel free to ask any further questions you might have
Regards

Hi Malavika Saju,
In the question we are told that R is true. 
From statement 1, we can say that P and Q both can't be true. The second statement is not directly dependent on R. It is dependent on P.
Let's draw a table varying the P and Q value and see how the values of R and  S changes.
From the table, we can say that Q is not always false. So, option A is incorrect.
In the first row, S is false but Q is true. So, option B is incorrect.
In the second row, S is true but Q is false. So, option C is also incorrect.
In the table, wherever S is true Q is false. So, option D is correct.
I hope this helps!!

HI Ritika Bagokar,
The value of R doesn't eliminate many cases. The only condition we have on R is it cannot be true if both P and Q are true.
In all the other cases, the value of R can be true or false.
Here, is the explanation for the question.
We are given that if both P and Q are true, then R is false; and if P is false, then S is false. Given that R is true, it follows that both P and Q are not true.

Now, let's consider the options:

(A) If R is true, then P can be false, Q can be false, or both P and Q can be false. Therefore, there are cases where Q can be true as well, so this statement is not always true.

(B) If S is false, then P can be true or false, and the implication is not bidirectional. Even if P were true, S can still be false. Hence, there are no additional restrictions compared to option A; P can be both true or false.

(C) If S is true, then P is definitely true, because if P were false, S would have been false. Given S is true, P is true, and R is false. If both P and Q were true, R would have been false, meaning one of P or Q is false. Since P is true, Q must be false. This option states that Q is true, so we can eliminate it.

(D) Using the logic from option C, if S is true, then Q must be false. This makes option D our answer.
Hope this helps!
Please feel free to ask any further questions you might have
Regards