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

Explanation:

Step1: Analyze the truth - value of each simple statement

• For \(p:-3 - 2=-5\), since \(-3-2=-(3 + 2)=-5\), \(p\) is True.
• For \(q\): Vertical angles are congruent. By the vertical - angle theorem, \(q\) is True.
• For \(r:2 + 8>10\), since \(2+8 = 10\), \(r\) is False. Then \(\sim r\) (the negation of \(r\)) is True.

Step2: Analyze the compound statement \(q\vee\sim r\)

The symbol \(\vee\) represents a disjunction. A disjunction \(A\vee B\) is True if either \(A\) is True, \(B\) is True, or both \(A\) and \(B\) are True.
Here \(q\) is True and \(\sim r\) is True.

Answer:

Vertical angles are congruent, or \(2 + 8\) is not greater than \(10\);
\(q\) is True, and \(\sim r\) is True, so \(q\vee\sim r\) is True.