Question

directions: use the statements below along with the diagram to write compound statements. then give its truth - value. p: points c, e, and b are collinear. q: ∠aec≅∠deb r: ef is the angle bisector of ∠aed s: ∠bec is an acute angle. 1. p ∨ q: ______ truth value: ______

Explanation:

Step1: Recall the meaning of 'or' in logic

The symbol $\vee$ represents a disjunction (or - statement). A disjunction $p\vee q$ is true if either $p$ is true, $q$ is true, or both are true.

Step2: Analyze the truth - value of $p$

Points $C$, $E$, and $B$ lie on the same straight line, so $p$: "Points $C$, $E$, and $B$ are collinear" is true.

Step3: Analyze the truth - value of $q$

$\angle AEC$ and $\angle DEB$ are vertical angles. Vertical angles are congruent, so $q$: "$\angle AEC\cong\angle DEB$" is true.

Step4: Determine the truth - value of $p\vee q$

Since both $p$ and $q$ are true, by the definition of a disjunction, $p\vee q$ is true.

Answer:

$p\vee q$: Points $C$, $E$, and $B$ are collinear or $\angle AEC\cong\angle DEB$
Truth Value: True