Question

1. whats the truth value of: \even numbers are multiples of 3 and even numbers are multiples of 2, or circles have 180 degrees\.

Explanation:

To determine the truth value of the compound statement (let's parse the statement properly: it seems to be a disjunction? Wait, the original text might have a typo, but let's assume we have two statements:

Let \( p \): "even numbers are multiples of 3"
Let \( q \): "even numbers are multiples of 2"
Let \( r \): "circles have 180 degrees" (though a straight angle is 180°, a circle is 360°, but maybe the statement is about something else, but let's focus on the first part about even numbers)

Step 1: Analyze \( p \): "even numbers are multiples of 3"

Even numbers are integers divisible by 2 (e.g., 2, 4, 6, 8, ...). A multiple of 3 is divisible by 3 (e.g., 3, 6, 9, ...). Most even numbers (e.g., 2, 4, 8) are not multiples of 3. So \( p \) is false.

Step 2: Analyze \( q \): "even numbers are multiples of 2"

By definition, an even number is an integer that is divisible by 2 (i.e., a multiple of 2). So \( q \) is true.

Step 3: Analyze the compound statement (assuming it’s a disjunction \( p \lor q \) or \( q \lor \dots \))

If the statement is \( p \lor q \) (or focuses on \( q \)):

• A disjunction \( A \lor B \) is true if at least one of \( A \) or \( B \) is true.
• Since \( q \) is true, \( p \lor q \) is true.

(Note: The "circles have 180 degrees" part is false (a circle has 360°), but if the main focus is on even numbers, the key true statement is \( q \).)

Answer:

The statement "even numbers are multiples of 2" is true, so the compound statement (if including this) is true. If the full statement is a disjunction with this true part, the truth value is \(\boldsymbol{\text{True}}\).