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
~ r ∨ ~ p
2 + 8 select choice 10 select choice -3 - 2 select choice -5;
~ r is select choice, and ~ p is select choice, so ~ r ∨ ~ p is select choice.

Explanation:

Step1: Determine the truth value of \(p\)

\(-3 - 2=-5\), so \(p\) is true. Then \(\sim p\) (the negation of \(p\)) is false.

Step2: Determine the truth value of \(r\)

\(2 + 8=10\), and \(10>10\) is false. So \(r\) is false. Then \(\sim r\) (the negation of \(r\)) is true.

Step3: Determine the truth value of \(\sim r\vee\sim p\)

For a disjunction \(A\vee B\), the statement is true if at least one of \(A\) or \(B\) is true. Here \(A = \sim r\) (true) and \(B=\sim p\) (false).

Answer:

\(2 + 8\) \(
ot> \) \(10\) \(\text{or}\) \(-3 - 2\) \(
eq\) \(-5\); \(\sim r\) is \(\text{true}\), and \(\sim p\) is \(\text{false}\), so \(\sim r\vee\sim p\) is \(\text{true}\).