GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 3

Answer 1

My approach :

Using A → B = A’ V B

(S → R) ^ (R → S) hence option b is directly an english interpretation of this hence correct.

Now (S → R) ^ (R → S) = S ↔ R meaning S = R so option c is also correct.

 

We know, biimplication is same as xor’ but option d means xor so incorrect.

In option a, R ↔ S’  Is wrong again.

 

Answer 2

Answer 3

Detailed Video Solution: https://youtu.be/nclBhBmtz2g?t=23

$(\text{R} \vee \neg \text{S} )\wedge (\neg \text{R} \vee \text{S})$ is equivalent to $\text{R} \leftrightarrow \text{S}$.

Hence, B; C is correct.

Answer 4

Given atomic propositions:

• $R$: It is Raining
• $S$: Sonu is Sick

Logical expression: $(R \vee \neg S) \wedge (\neg R \vee S) \equiv R ↔S$

• A. It is raining if and only if sonu is not sick $\equiv$ $R ↔ \neg S \equiv (\neg R \vee \neg S) \wedge (S \vee R)$
• B. If sonu is sick then it is raining, and vice versa $\equiv S ↔ R \equiv (\neg S \vee R) \wedge (\neg R \vee S)$ [Equivalent to given logical expression]
• C. It is raining is equivalent to sonu is sick $\equiv R ↔ S \equiv (\neg R \vee S) \wedge (\neg S \vee R)$ [Equivalent to given logical expression]
• D. It is raining or sonu is sick but not both $\equiv R \bigoplus S \equiv (R \wedge \neg S) \vee (S \wedge \neg R)$    

Ans: B;C