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logic based statement

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Determine which if any of the three statements are equivalent.

1)If the carpet is not clean, then Sheila will run the vacuum.
2)If it is not case that both the carpet is clean and Sheila will run the vacuum.
3)If the carpet is clean, then Sheila will not run the vauuum.

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Solution Summary

The solution provides detailed explanation how to check logical statement.

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Let p=the carpet is clean and q=sheila will run the vacuum.
I) ~p --> q
II) ~(p and q)
III) p ---> ~q

let p=t and q = t

I) ~t --> f = f ---> f = True statement
II) ~(t and t) = ~ t = f = False Statement
III) ...

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