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: ____ 2. q ∧ s: ____ truth value: ____ 3. ∼p ∧ r: ____ truth value: ____ 4. r ∨ ∼s: ____ truth value: ____ 5. ∼q ∧ ∼r: ____ truth value: ____ 6. p ∨ ∼q: ____ truth value: ____ 7. ∼r ∨ ∼s: ____ truth value: ____ 8. ∼q ∧ s: ____ truth value: ____ 9. p ∨ r: ____ truth value: ______

Explanation:

1.

Step1: Analyze p

Points C, E, and B are not collinear, so p is False.

Step2: Analyze q

Vertical - angles ∠AEC and ∠DEB are congruent, so q is True.

Step3: Use or - logic

In p ∨ q, if at least one of p or q is True, the compound statement is True. Since q is True, p ∨ q is True.

2.

Step1: Analyze q

∠AEC and ∠DEB are vertical - angles and are congruent, so q is True.

Step2: Analyze s

From the diagram, ∠BEC is an acute angle, so s is True.

Step3: Use and - logic

In q ∧ s, both q and s must be True for the compound statement to be True. Since both are True, q ∧ s is True.

3.

Step1: Analyze ~p

Points C, E, and B are not collinear, so ~p is True.

Step2: Analyze r

From the diagram, $\overrightarrow{EF}$ is not the angle - bisector of ∠AED, so r is False.

Step3: Use and - logic

In ~p ∧ r, both ~p and r must be True for the compound statement to be True. Since r is False, ~p ∧ r is False.

4.

Answer:

Points C, E, and B are collinear or ∠AEC ≅ ∠DEB; True