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 q ∨ ~r q is select choice, and ~r is select choice, so q ∨ ~r is select choice. vertical angles are congruent. select choice 2 + 8>10. select choice incorrect 1 try left. try once more

Explanation:

Step1: Analyze statement p

Calculate $-3 - 2=-5$, so statement $p$ is true.

Step2: Analyze statement q

Vertical angles are congruent by definition, so statement $q$ is true.

Step3: Analyze statement r

Calculate $2 + 8=10$, and $10
gtr10$, so statement $r$ is false.

Step4: Form compound - statement and find truth - value

We want to form $q\vee\sim r$. Since $r$ is false, $\sim r$ is true. The disjunction $q\vee\sim r$ is true because if either $q$ or $\sim r$ is true (and here both $q$ and $\sim r$ are true), the disjunction is true.

Answer:

The compound statement $q\vee\sim r$ is true.