Question

If \( p \): 2 is an even number, \( q \): 2 is a prime number, and \( r \): \( 2 + 2 = 2^2 \), then the symbolic statement \( p \rightarrow (q \vee r) \) means:

• A. 2 is an even number and 2 is a prime number or \( 2 + 2 = 2^2 \)
• B. 2 is an even number then 2 is a prime number or \( 2 + 2 = 2^2 \)
• C. 2 is an even number or 2 is a prime number then \( 2 + 2 = 2^2 \)
• D. If 2 is not an even number then 2 is a prime number \(\alpha\) = \( 2 + 2 = 2^2 \)

Hint:

Understanding logical implications helps in interpreting symbolic statements correctly.

Answer 1

The Correct Option is B

The given symbolic statement: \[ p \rightarrow (q \vee r) \] By definition of implication: \[ p \rightarrow (q \vee r) \equiv \neg p \vee (q \vee r) \] Since \( p \) represents "2 is an even number," the statement translates to: "If 2 is an even number, then 2 is a prime number or \( 2 + 2 = 2^2 \)."

Answer 2

Step 1: Understanding the logical statements
We are given the following propositions: 
- \( p \): 2 is an even number, 
- \( q \): 2 is a prime number, 
- \( r \): \( 2 + 2 = 2^2 \).

Step 2: Interpreting the symbolic statement
The given symbolic statement is: \[ p \rightarrow (q \vee r) \] This is a conditional statement, where: - \( p \) is the hypothesis ("2 is an even number"), - \( q \vee r \) is the conclusion ("2 is a prime number or \( 2 + 2 = 2^2 \)").

The logical meaning of this statement is: "If 2 is an even number, then 2 is a prime number or \( 2 + 2 = 2^2 \)."

Step 3: Final Answer
The correct interpretation of the statement is:

2 is an even number then 2 is a prime number or \( 2 + 2 = 2^2 \)