Question:
Let \( p: \) I am brave, \( q: \) I will climb the Mount Everest. The symbolic form of a statement, 'I am neither brave nor I will climb the Mount Everest' is:
Let \( p: \) I am brave, \( q: \) I will climb the Mount Everest. The symbolic form of a statement, 'I am neither brave nor I will climb the Mount Everest' is:
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In symbolic logic, the phrase "neither...nor" translates to \( \neg p \land \neg q \). Always apply negation rules carefully for accurate representation.
Updated On: Jan 22, 2025
- \( p \land q \)
- \( \sim (p \land q) \)
- \( \sim p \land \sim q \)
- \( \sim p \land q \)
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The Correct Option is C
Solution and Explanation
The statement "I am neither brave nor will I climb Mount Everest" can be reworded as:
\[
\text{"Not brave and will not climb Mount Everest."}
\]
Let \( p: \) I am brave and \( q: \) I will climb Mount Everest. Therefore: \[ \text{Not brave} \implies \neg p, \quad \text{and} \quad \text{Will not climb Mount Everest} \implies \neg q. \]
Combining these using "and" (\( \land \)): \[ \neg p \land \neg q. \]
Hence, the symbolic representation of the statement is: \[ \boxed{\neg p \land \neg q}. \]
Let \( p: \) I am brave and \( q: \) I will climb Mount Everest. Therefore: \[ \text{Not brave} \implies \neg p, \quad \text{and} \quad \text{Will not climb Mount Everest} \implies \neg q. \]
Combining these using "and" (\( \land \)): \[ \neg p \land \neg q. \]
Hence, the symbolic representation of the statement is: \[ \boxed{\neg p \land \neg q}. \]
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