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 ∨ q 2 + 8 > 10, select choice vertical angles are congruent; r is select choice and q is select choice, so r ∨ q is select choice

Explanation:

Step1: Evaluate truth - value of r

Calculate \(2 + 8=10\), so the statement \(r:2 + 8>10\) is false.

Step2: Evaluate truth - value of q

The statement \(q\): Vertical angles are congruent is a well - known geometric fact and is true.

Step3: Evaluate \(r\vee q\)

In a disjunction \(A\vee B\), if at least one of \(A\) or \(B\) is true, then \(A\vee B\) is true. Since \(q\) is true, \(r\vee q\) is true.

Answer:

\(2 + 8>10\) or vertical angles are congruent; \(r\) is false, and \(q\) is true, so \(r\vee q\) is true.