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 and q
-3 - 2 = -5, select choice vertical angles select choice congruent;
p is select choice, and q is select choice, so p and q is select choice.

Explanation:

Step1: Determine the truth - value of \(p\)

Calculate \(-3 - 2\). Using the rule of subtraction \(a-b=a+( - b)\), we have \(-3-2=-3+( - 2)=-(3 + 2)=-5\). So \(p\) is a true statement.

Step2: Determine the truth - value of \(q\)

By the vertical - angles theorem, vertical angles are congruent. So \(q\) is a true statement.

Step3: Determine the truth - value of \(p\) and \(q\)

For a conjunction \(p\land q\) (where \(p\) and \(q\) are statements), the rule is \(p\land q\) is true if and only if both \(p\) and \(q\) are true. Since \(p = T\) (true) and \(q = T\) (true), \(p\land q=T\).

Answer:

\(-3 - 2=-5\), and vertical angles are congruent; \(p\) is true, and \(q\) is true, so \(p\) and \(q\) is true.