UGC NET CSE | August 2024 | Part 2 | Question: 75

Question

Consider the following if $p$ and $q$ are two statements.

1. $\sim(\mathrm{p} \wedge \mathrm{q}) \equiv \sim \mathrm{p} \vee \sim \mathrm{q}$
2. $\sim(\mathrm{p} \vee \mathrm{q}) \equiv \sim \mathrm{p} \wedge \sim \mathrm{q}$
3. $\mathrm{p} \wedge \sim \mathrm{p} \equiv \mathrm{T}$
4. $\sim(\mathrm{p} \Rightarrow \mathrm{q}) \equiv \mathrm{p} \wedge \sim \mathrm{q}$
5. $\mathrm{p} \vee \mathrm{q} \equiv \sim \mathrm{p} \vee \sim \mathrm{q}$

Choose the correct answer from the options given below:

• A. $(I), (II)$ and $(IV)$ Only
• B. $(I), (III)$ and $(IV)$ Only
• C. $(III), (IV)$ and $(V)$ Only
• D. $(I), (II)$ and $(III)$ Only

Answer 1

Option A

We can apply option elimination.

A and B parts are true so we check for part D whose LHS turns out to be ~(~p v q)= p ^ ~q = RHS.

A,B,D True so we conclude with ans A

Answer 2

A. Demorgan law

B. Demorgan law (Break the line change the sign)

C.P  intersection  P'  = 0 (false)

D . (P -> Q) ' = (P' v Q) ' = P intersection  Q' (True)

E. False;