Question

1. whats the truth value of the negation of: \triangles have 3 vertices and (2)(7) = 14\?

Explanation:

Step1: Identify the original statement structure

The original statement is a conjunction: \( P \land Q \), where \( P \) is "triangles have 3 vertices" and \( Q \) is "\( (2)(7)=14 \)".

Step2: Recall De Morgan's Law for negation of conjunction

De Morgan's Law states that \(
eg (P \land Q) \equiv
eg P \lor
eg Q \).

Step3: Evaluate the truth values of \( P \) and \( Q \)

• \( P \): Triangles by definition have 3 vertices, so \( P \) is true (\( T \)). Thus, \(

eg P \) is false (\( F \)).

• \( Q \): \( (2)(7) = 14 \) is a true arithmetic statement, so \( Q \) is true (\( T \)). Thus, \(

eg Q \) is false (\( F \)).

Step4: Evaluate \(

eg P \lor
eg Q \)
Using the truth table for disjunction (\( \lor \)): \( F \lor F = F \). Wait, no—wait, original statement \( P \land Q \): \( T \land T = T \). So negation of \( T \) is \( F \). Wait, let's recheck:

Wait, \( P \) is true, \( Q \) is true. So \( P \land Q \) is true. The negation of a true statement is false. But let's apply De Morgan's Law correctly. \(
eg (P \land Q) =
eg P \lor
eg Q \). \(
eg P \) is "triangles do not have 3 vertices" (false), \(
eg Q \) is "\( (2)(7)
eq 14 \)" (false). So \(
eg P \lor
eg Q \) is false \( \lor \) false = false. Which matches the negation of true (which is false).

Answer:

The truth value of the negation is \(\boldsymbol{\text{False}}\) (or \( F \)).