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: Analyze the truth value of \(r\)

For \(r:2 + 8>10\), since \(2+8 = 10\), the statement \(2 + 8>10\) is false. So \(r\) is false.

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

For \(q\): Vertical angles are congruent. This is a geometric theorem. So \(q\) is true.

Step3: Analyze the truth value of \(r\vee q\)

The disjunction \(p\vee q\) is defined as: \(p\vee q\) is true if either \(p\) is true, \(q\) is true, or both \(p\) and \(q\) are true.
Since \(r\) is false (\(F\)) and \(q\) is true (\(T\)), for \(r\vee q\), using the truth - table for disjunction (\(F\vee T=T\)).

Answer:

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