Question

For any two statements p and q, the negation of the expression p ∨ (~p ∧ q) is:
(A) p ⇔ q (B) ~ p ∨ ~q
(C) ~ p ∧ ~q (D) p ∧ q

Answer 1

Answer:

Option C is correct. .................... .

Answer 2

Option (C) is correct.

Step-by-step explanation:

We need to find the the negation of the expression p ∨ (~p ∧ q).

The negation of p ∨ (~p ∧ q) is ~(p ∨ (~p ∧ q)). Let's simplify it.

$\sim \left ( p\vee \left ( \sim p\wedge q \right ) \right )$

$\equiv \sim \left ( \left (p\vee \sim p \right )\wedge\left ( p\vee q \right ) \right )$, we know that $p\vee \sim p = True$

$\equiv \sim \left ( T\wedge\left ( p\vee q \right ) \right )$, we know that $True\wedge a = a$

$\equiv \sim \left ( p\vee q \right )$

$\equiv \sim p\wedge \sim q$

Hence, option (C) is correct.