Bright Fernandez
09/18/2024 · Primary School
The statement \( \sim P \wedge P \) is a contradiction?
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Yes, the statement \( \sim P \wedge P \) is indeed a contradiction.
To understand why, let's break it down:
- \( P \) is a proposition that can either be true (T) or false (F).
- \( \sim P \) is the negation of \( P \). If \( P \) is true, then \( \sim P \) is false, and if \( P \) is false, then \( \sim P \) is true.
Now, let's analyze the expression \( \sim P \wedge P \):
- If \( P \) is true (T), then \( \sim P \) is false (F), so \( \sim P \wedge P \) evaluates to \( F \wedge T \), which is false (F).
- If \( P \) is false (F), then \( \sim P \) is true (T), so \( \sim P \wedge P \) evaluates to \( T \wedge F \), which is also false (F).
In both cases, the expression \( \sim P \wedge P \) evaluates to false. Therefore, it is a contradiction, as it cannot be true under any circumstances.
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The statement \( \sim P \wedge P \) is a contradiction.
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