Question

determine the truth value for the statement when p is true, q is false, and r is false \
eg (p\vee q)\vee \
eg (p\vee r) choose the correct answer below. \circ the statement is true. \circ the statement is false.

Explanation:

Step1: Evaluate $p \land q$

Given $p=\text{true}$, $q=\text{false}$, so $p \land q = \text{true} \land \text{false} = \text{false}$.

Step2: Evaluate $

eg(p \land q)$
$
eg(p \land q) =
eg(\text{false}) = \text{true}$.

Step3: Evaluate $p \lor r$

Given $p=\text{true}$, $r=\text{false}$, so $p \lor r = \text{true} \lor \text{false} = \text{true}$.

Step4: Evaluate $

eg(p \lor r)$
$
eg(p \lor r) =
eg(\text{true}) = \text{false}$.

Step5: Evaluate the full statement

$
eg(p \land q) \land
eg(p \lor r) = \text{true} \land \text{false} = \text{false}$.

Answer:

The statement is false.