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:
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:
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Understanding logical implications helps in interpreting symbolic statements correctly.
Updated On: Mar 26, 2025
- 2 is an even number and 2 is a prime number or \( 2 + 2 = 2^2 \)
- 2 is an even number then 2 is a prime number or \( 2 + 2 = 2^2 \)
- 2 is an even number or 2 is a prime number then \( 2 + 2 = 2^2 \)
- If 2 is not an even number then 2 is a prime number \(\alpha\) = \( 2 + 2 = 2^2 \)
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The Correct Option is B
Solution and Explanation
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 \( 2 + 2 = 2^2 \)."
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