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
p ∧ r

• 3 - 2=-5, select choice 2 + 8>10, select choice, and r is select choice, so p ∧ r is select choice.

Explanation:

Step1: Solve for \(p\)

Given \(p - 3-2=-5\), simplify the left - hand side: \(p-(3 + 2)=-5\), so \(p-5=-5\). Add 5 to both sides: \(p=-5 + 5=0\). The statement \(p:-3-2=-5\) is True (\(T\)) since \(-3-2=-5\).

Step2: Solve for \(r\)

Given \(r:2 + 8>10\), calculate \(2+8 = 10\). Since \(10
ot>10\), the statement \(r:2 + 8>10\) is False (\(F\)).

Step3: Evaluate \(p\wedge r\)

The logical AND (\(\wedge\)) operation: \(p\wedge r\) is True only when both \(p\) and \(r\) are True. Since \(p = T\) and \(r = F\), \(p\wedge r\) is False.

Answer:

\(p\) is True, \(r\) is False, and \(p\wedge r\) is False.