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 statement r

Calculate $2 + 8=10$, so $2 + 8>10$ is false. Thus, $r$ is false.

Step2: Evaluate statement q

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

Step3: Determine truth - value of disjunction

For a disjunction $r\vee q$, if at least one of $r$ or $q$ is true, then $r\vee q$ 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.