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~((~(~p))^^q) is equal to...

`~((~(~p))^^q) ` is equal to

A

`~p^^q`

B

`~pvv~q`

C

`p^^~q`

D

`~p^^~q`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression `~((~(~p))^^q)`, we will simplify it step by step using logical identities. ### Step-by-Step Solution: 1. **Identify the innermost negation**: We start with the expression `~(~(~p))^^q`. The innermost part is `~p`. 2. **Apply the double negation law**: According to the double negation law, `~~p` is equivalent to `p`. Therefore, we can simplify `~(~p)` to `p`. - So, `~(~(~p))` becomes `~p`. **Expression now**: `~(p^^q)` 3. **Apply De Morgan's Law**: De Morgan's Law states that `~(A^^B)` is equivalent to `~A v ~B`. In our case, `A` is `p` and `B` is `q`. - So, `~(p^^q)` becomes `~p v ~q`. **Final Expression**: `~p v ~q` Thus, the expression `~((~(~p))^^q)` simplifies to `~p v ~q`. ### Final Answer: `~p v ~q` ---
To solve the expression `~((~(~p))^^q)`, we will simplify it step by step using logical identities. ### Step-by-Step Solution: 1. **Identify the innermost negation**: We start with the expression `~(~(~p))^^q`. The innermost part is `~p`. 2. **Apply the double negation law**: ...
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