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~(pvv(~p)) is equal to...

`~(pvv(~p))` is equal to

A

`~pvvq`

B

`(~p)^^q`

C

`~pvv~p`

D

`~p^^~q`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression `~(p ∨ ~p)`, we will use logical identities and properties. Let's break it down step by step. ### Step-by-Step Solution: 1. **Identify the Expression**: The expression we need to simplify is `~(p ∨ ~p)`. 2. **Apply the Law of Excluded Middle**: According to the law of excluded middle, for any proposition `p`, the statement `p ∨ ~p` is always true. This means that `p ∨ ~p` evaluates to `True`. - **Result**: `p ∨ ~p = True` 3. **Negate the True Statement**: Now we need to negate the result from the previous step. Since we have established that `p ∨ ~p` is `True`, we can now apply negation. - **Result**: `~(True) = False` 4. **Final Result**: Therefore, the expression `~(p ∨ ~p)` simplifies to `False`. ### Conclusion: The expression `~(p ∨ ~p)` is equal to `False`.
To solve the expression `~(p ∨ ~p)`, we will use logical identities and properties. Let's break it down step by step. ### Step-by-Step Solution: 1. **Identify the Expression**: The expression we need to simplify is `~(p ∨ ~p)`. 2. **Apply the Law of Excluded Middle**: According to the law of excluded middle, for any proposition `p`, the statement `p ∨ ~p` is always true. This means that `p ∨ ~p` evaluates to `True`. ...
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