Answer to Question #152261 in Discrete Mathematics for kutub

Question

If p is true, q, r, and s are false, find the truth value of the proposition.

¬(¬𝑝 ∨ 𝑞) ∨ ¬((𝑝 ∧ ¬𝑟) → ¬𝑠)

Answer 1

$\text {let True is 1; False is 0; then}$

$¬(¬𝑝 ∨ 𝑞) ∨ ¬((𝑝 ∧ ¬𝑟) → ¬𝑠) =$

$¬(¬1 ∨ 0) ∨ ¬((1 ∧ ¬0) → ¬0)=$

$¬(0 ∨ 0) ∨ ¬((1 ∧ 1) → 1)=$

$¬(0 ) ∨ ¬(1 → 1)=1∨ ¬(0)=1∨ 1= 1;$

$¬(¬𝑝 ∨ 𝑞) ∨ ¬((𝑝 ∧ ¬𝑟) → ¬𝑠)= 1 \text{ is True}$

Answer: $¬(¬𝑝 ∨ 𝑞) ∨ ¬((𝑝 ∧ ¬𝑟) → ¬𝑠) \text{ is True}$