Question

let p and q represent the following statements.
p: 2 + 9 = 11
q: 10 × 8 = 80
determine the truth value for the statement ~p∨~q.
choose the correct truth value below.
○ ~p∨~q is false.
○ ~p∨~q is true.

Explanation:

Step1: Evaluate truth value of p

$2+9=11$ is true, so $p = \text{True}$

Step2: Evaluate truth value of $\boldsymbol{\sim p}$

$\sim p$ (negation of p) is $\text{False}$

Step3: Evaluate truth value of q

$10 \times 8=80$ is true, so $q = \text{True}$

Step4: Evaluate truth value of $\boldsymbol{\sim q}$

$\sim q$ (negation of q) is $\text{False}$

Step5: Evaluate $\boldsymbol{\sim p \lor \sim q}$

A disjunction $\lor$ is true only if at least one operand is true. Here both are false, so $\sim p \lor \sim q = \text{False}$

Answer:

~p∨~q is false.