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 symbolic statement provided is: \[ p \rightarrow (q \vee r) \] According to the definition of implication, this is equivalent to: \[ p \rightarrow (q \vee r) \equiv eg p \vee (q \vee r) \] Given that \( p \) signifies "2 is an even number," the statement can be rephrased as: "If 2 is an even number, then 2 is a prime number or \( 2 + 2 = 2^2 \)."