Question

Directions: Use the statements below along with the diagram to write compound statements. Then find its truth value. p: Points C, E, and B are collinear. q: ZAEC ZDEB r: EF is the angle bisector of ZAED s: ZBEC is an acute angle. Symbolic pvq q^s ~p Ar rv ~s ~q A ~r PV ~q Written Compound Statement Truth Value ​

Answer 1

Explanation:

Answer 2

The compound statements and truth value are given below:

To complete the table using logical operators and determining the truth value of each compound statement, we'll first need to define the symbols:

- p : Points C, E, and B are collinear.

- q : Angle AEC is congruent to angle DEB.

- r : EF is the angle bisector of angle AED.

- s : Angle BEC is an acute angle.

The symbolic column contains logical operations. Here's what they mean and how we can construct the written compound statements:

1.
`\( p \lor q \):`This is a logical OR operation. The written compound statement is "Points C, E, and B are collinear OR angle AEC is congruent to angle DEB."

2.
`\( q \land s \):`This is a logical AND operation. The written compound statement is "Angle AEC is congruent to angle DEB AND angle BEC is an acute angle."

3.
`\( \\eg p \land r \):` This is a logical NOT AND operation. The written compound statement is "It is not true that points C, E, and B are collinear AND EF is the angle bisector of angle AED."

4.
`\( r \lor \\eg s \):`This is a logical OR NOT operation. The written compound statement is "EF is the angle bisector of angle AED OR it is not true that angle BEC is an acute angle."

5.
`\( \\eg q \land \\eg r \):` This is a logical NOT AND NOT operation. The written compound statement is "It is not true that angle AEC is congruent to angle DEB AND it is not true that EF is the angle bisector of angle AED."

6.
`\( p \lor \\eg q \):`This is a logical OR NOT operation. The written compound statement is "Points C, E, and B are collinear OR it is not true that angle AEC is congruent to angle DEB."