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;
p is true, and r is false, so p ∧ r is false

Explanation:

Step1: Evaluate \(p\)

Calculate \(-3 - 2\). Using the rule of subtraction of integers, \(-3-2=- (3 + 2)=-5\). So \(p\) is true.

Step2: Evaluate \(r\)

Calculate \(2 + 8\). \(2+8 = 10\). The inequality \(2 + 8>10\) (i.e., \(10>10\)) is false.

Step3: Evaluate \(p\land r\)

For a conjunction \(p\land r\), the compound statement is true if and only if both \(p\) and \(r\) are true. Since \(p\) is true and \(r\) is false, by the definition of conjunction (\(T\land F = F\)), \(p\land r\) is false.

Answer:

\(-3 - 2=-5\) and \(2 + 8>10\); \(p\) is true, \(r\) is false, so \(p\land r\) is false