Question

use the statements to write a compound statement for the conjunction or disjunction. then find the truth values.
p: -3 - 2 = -5
q: vertical angles are congruent.
r: 2 + 8 > 10
~p ∧ ~q
-3 - 2 select choice -5, and select choice are congruent; ~p is select choice, and ~q is select choice.
so ~p ∧ ~q is select choice.

Explanation:

Step1: Analyze the truth - value of \(p\)

Given \(p:-3 - 2=-5\). Since \(-3-2=-(3 + 2)=-5\), \(p\) is True. Then \(\sim p\) (the negation of \(p\)) is False.

Step2: Analyze the truth - value of \(q\)

Given \(q:\) Vertical angles are congruent. By the vertical - angle theorem, vertical angles are congruent. So \(q\) is True. Then \(\sim q\) (the negation of \(q\)) is False.

Step3: Analyze the truth - value of \(\sim p\wedge\sim q\)

The logical conjunction \(A\wedge B\) is True when both \(A\) and \(B\) are True. Here \(A = \sim p\) and \(B=\sim q\). Since \(\sim p=\text{False}\) and \(\sim q=\text{False}\), using the rule for conjunction \(T\wedge T=T\), \(T\wedge F = F\), \(F\wedge T=F\), \(F\wedge F = F\)

Answer:

\(-3 - 2
eq-5\), and vertical angles are not congruent; \(\sim p\) is False, and \(\sim q\) is False, so \(\sim p\wedge\sim q\) is False.