Question

Given the statements:

p: Points C, E, and B are collinear.
q: Angle AEC is perpendicular to angle DEB.
r: EF is the angle bisector of angle AED.
s: BEC is an acute angle.

What is the compound statement formed by p v q, and what is its truth value?

Answer 1

The compound statement formed by p ∨ q is "Points C, E, and B are collinear or angle AEC is perpendicular to angle DEB." This statement is true.

Step-by-step explanation:

The symbol ∨ represents the logical connective "or." Therefore, the compound statement p ∨ q is true if either p or q is true.

In this case, statement p states that "Points C, E, and B are collinear." Since points C, E, and B are collinear, statement p is true. Therefore, the compound statement p ∨ q is true.

Alternatively, we could evaluate the truth value of the compound statement by evaluating the truth values of its individual components. Statement p is true, and statement q is false (since angle AEC is not perpendicular to angle DEB). Therefore, the compound statement p ∨ q is true (since a statement connecting two statements with "or" is true if either statement is true).