TIFR CSE 2023 | Part B | Question: 1

Question

Consider the following two statements:

• $\text{(P)}$ The current population of Bhutan is greater than the current population of India.
• $\text{(Q)}$ The Moon is smaller than the Earth.

Clearly, $\text{(P)}$ is false, while $\text{(Q)}$ is true. Which of the following logical statements evaluates to true?

• A. $\neg \text{P} \Rightarrow \text{Q}$
• B. $\text{Q} \Rightarrow \text{P}$
• C. $\neg(\text{P} \Rightarrow \text{Q})$
• D. $\text{P} \Leftrightarrow \text{Q}$
• E. None of the above

Answer 1

Given, $P = False$  and  $Q = True$

 

A. ~P → Q  $\Rightarrow$ True → True $\Rightarrow$ True

​​​​​​​B. Q → P $\Rightarrow$  True → False $\Rightarrow$ False

​​​​​​​C. ~(P → Q) $\Rightarrow$  ~ (False → True) $\Rightarrow$ ~True $\Rightarrow$ False

​​​​​​​D. P ↔ Q $\Rightarrow$ P ⊙ Q $\Rightarrow$ False ⊙ True $\Rightarrow$ False

 

Correct Ans : Option A.

Answer 2

Truth Value of P : False

Truth Value of Q : True

A) (~P $\Rightarrow$ Q) $\equiv$ ( ~F $\Rightarrow$ T) $\equiv$ (T $\Rightarrow$ T) $\equiv$ True

B)( Q $\Rightarrow$ P) $\equiv$ (T $\Rightarrow$ F) $\equiv$ False

C) ~(P $\Rightarrow$ Q) $\equiv$ ~(F $\Rightarrow$ T) $\equiv$ ~T $\equiv$ False

D) (P $\Leftrightarrow$ Q) $\equiv$ (F $\Leftrightarrow$ T) $\equiv$ False

Hence , A) is the correct answer