Evaluate the truth of the proposition ~P ∧ Q.
Understand the Problem
The question involves evaluating a logical proposition based on given statements P and Q. Specifically, it asks whether the negation of the conjunction of these two statements is true or false.
Answer
The answer is True.
Answer for screen readers
The final answer is True.
Steps to Solve
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Evaluate Statements P and Q Determine the truth values of statements P and Q.
- Statement P: (1 + 1 = 2) is True.
- Statement Q: A 12-year-old girl is older than her 16-year-old sister is False.
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Determine the Conjunction (P \land Q) The conjunction (P \land Q) is true only if both P and Q are true.
- Since P is True and Q is False, (P \land Q) is False.
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Negate the Conjunction (\sim (P \land Q)) Find the negation of the conjunction.
- The negation of False is True.
- Therefore, (\sim (P \land Q)) is True.
The final answer is True.
More Information
The proposition evaluates the negation of a conjunction. Understanding conjunctions and negations is key in logic statements. Here, even if one part of the conjunction is false, the whole conjunction is false, and its negation is true.
Tips
- A common mistake is misinterpreting the conjunction. Remember that (P \land Q) is only true if both P and Q are true.
- Confusing the negation; some may think that negating a false statement results in false, rather than true.
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