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: ∠aec = ∠deb
r: ef is the angle - bisector of ∠aed
s: ∠bec is an acute angle.
1. p ∨ q
truth value:
2.
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:

Question

Accepted Answer

1. **$p\vee q$**:
   - **Explanation**:
     - The symbol $\vee$ represents the logical - OR operation. The compound statement $p\vee q$ means “Points $C$, $E$, and $B$ are collinear or $\angle AEC\cong\angle DEB$”.
     - Without seeing the actual diagram, assume that if $p$ is true or $q$ is true or both are true, the compound statement is true. Let's assume from a general geometric perspective, if $p$ is false and $q$ is true (vertically - opposite angles are always equal, so $q$ is likely to be true in a non - degenerate case), then $p\vee q$ is true.
   - **Answer**: The compound statement is “Points $C$, $E$, and $B$ are collinear or $\angle AEC\cong\angle DEB$”. Truth Value: True (assuming $q$ is true as $\angle AEC$ and $\angle DEB$ are vertically - opposite angles).
2. **$
eg p\wedge r$**:
   - **Explanation**:
     - $
eg p$ means “Points $C$, $E$, and $B$ are not collinear”, and $\wedge$ represents the logical - AND operation. The compound statement $
eg p\wedge r$ means “Points $C$, $E$, and $B$ are not collinear and $EF$ is the angle bisector of $\angle AED$”.
     - For $
eg p\wedge r$ to be true, both $
eg p$ and $r$ must be true. If $p$ is false (points are not collinear) and $r$ is true ( $EF$ is the angle bisector of $\angle AED$), then the compound statement is true.
   - **Answer**: The compound statement is “Points $C$, $E$, and $B$ are not collinear and $EF$ is the angle bisector of $\angle AED$”. Truth Value: Depends on the diagram (if $
eg p$ is true and $r$ is true, then True; otherwise False).
3. **$r\vee
eg s$**:
   - **Explanation**:
     - $
eg s$ means “$\angle BEC$ is not an acute angle”. The compound statement $r\vee
eg s$ means “$EF$ is the angle bisector of $\angle AED$ or $\angle BEC$ is not an acute angle”.
     - For $r\vee
eg s$ to be true, either $r$ is true or $
eg s$ is true or both are true.
   - **Answer**: The compound statement is “$EF$ is the angle bisector of $\angle AED$ or $\angle BEC$ is not an acute angle”. Truth Value: Depends on the diagram.
4. **$
eg q\wedge
eg r$**:
   - **Explanation**:
     - $
eg q$ means “$\angle AEC
ot\cong\angle DEB$” and $
eg r$ means “$EF$ is not the angle bisector of $\angle AED$”. The compound statement $
eg q\wedge
eg r$ means “$\angle AEC
ot\cong\angle DEB$ and $EF$ is not the angle bisector of $\angle AED$”.
     - For $
eg q\wedge
eg r$ to be true, both $
eg q$ and $
eg r$ must be true.
   - **Answer**: The compound statement is “$\angle AEC
ot\cong\angle DEB$ and $EF$ is not the angle bisector of $\angle AED$”. Truth Value: Depends on the diagram.
5. **$p\vee
eg q$**:
   - **Explanation**:
     - $
eg q$ means “$\angle AEC
ot\cong\angle DEB$”. The compound statement $p\vee
eg q$ means “Points $C$, $E$, and $B$ are collinear or $\angle AEC
ot\cong\angle DEB$”.
     - For $p\vee
eg q$ to be true, either $p$ is true or $
eg q$ is true or both are true.
   - **Answer**: The compound statement is “Points $C$, $E$, and $B$ are collinear or $\angle AEC
ot\cong\angle DEB$”. Truth Value: Depends on the diagram.
6. **$
eg r\vee
eg s$**:
   - **Explanation**:
     - $
eg r$ means “$EF$ is not the angle bisector of $\angle AED$” and $
eg s$ means “$\angle BEC$ is not an acute angle”. The compound statement $
eg r\vee
eg s$ means “$EF$ is not the angle bisector of $\angle AED$ or $\angle BEC$ is not an acute angle”.
     - For $
eg r\vee
eg s$ to be true, either $
eg r$ is true or $
eg s$ is true or both are true.
   - **Answer**: The compound statement is “$EF$ is not the angle bisector of $\angle AED$ or $\angle BEC$ is not an acute angle”. Truth Value: Depends on the diagram.
7. **$
eg q\wedge s$**:
   - **Explanation**:
     - $
eg q$ means “$\angle AEC
ot\cong\angle DEB$” and $s$ means “$\angle BEC$ is an acute angle”. The compound statement $
eg q\wedge s$ means “$\angle AEC
ot\cong\angle DEB$ and $\angle BEC$ is an acute angle”.
     - For $
eg q\wedge s$ to be true, both $
eg q$ and $s$ must be true.
   - **Answer**: The compound statement is “$\angle AEC
ot\cong\angle DEB$ and $\angle BEC$ is an acute angle”. Truth Value: Depends on the diagram.
8. **$p\vee r$**:
   - **Explanation**:
     - The compound statement $p\vee r$ means “Points $C$, $E$, and $B$ are collinear or $EF$ is the angle bisector of $\angle AED$”.
     - For $p\vee r$ to be true, either $p$ is true or $r$ is true or both are true.
   - **Answer**: The compound statement is “Points $C$, $E$, and $B$ are collinear or $EF$ is the angle bisector of $\angle AED$”. Truth Value: Depends on the diagram.

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