Question

use the given statements.
p: (-4)^2 > 0
q: an isosceles triangle has at least two congruent sides.
r: two angles, whose measure have a sum of 90, are supplements.
select the truth value of (p ∧ q) ∨ r.
select choice
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Explanation:

Step1: Determine truth - value of p

Calculate $(-4)^2 = 16$, and $16>0$. So $p$ is True.

Step2: Determine truth - value of q

By the definition of an isosceles triangle, it has at least two congruent sides. So $q$ is True.

Step3: Determine truth - value of $p\land q$

The conjunction $p\land q$ is True when both $p$ and $q$ are True. Since $p = T$ and $q = T$, then $p\land q=T$.

Step4: Determine truth - value of r

Two angles whose sum is 90 are complementary, not supplementary (supplementary angles have a sum of 180). So $r$ is False.

Step5: Determine truth - value of $(p\land q)\lor r$

The disjunction $A\lor B$ is True if either $A$ or $B$ (or both) is True. Here $A = p\land q=T$ and $B = r = F$. So $(p\land q)\lor r$ is True.

Answer:

True