Please check my Truth Table

Is this true or false if P is false and Q is true
~ ( ~ P OR Q ) AND ( ~ P OR ~ ( P AND ~ Q ) )

Work:

~ ( ~ P OR Q ) is F
~ ( P AND ~ Q ) is T

( ~ P OR ~ ( P AND ~ Q ) ) is T
~ ( ~ P OR Q ) AND ( ~ P OR ~ ( P AND ~ Q ) ) is False

You're right.

Quote:

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Work:

~ ( ~ P OR Q ) is F

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With this you can conclude. :)

Quote:

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Originally Posted by aeubz

Is this true or false if P is false and Q is true
~ ( ~ P OR Q ) AND ( ~ P OR ~ ( P AND ~ Q ) )
Work:
~ ( ~ P OR Q ) is F
~ ( P AND ~ Q ) is T
( ~ P OR ~ ( P AND ~ Q ) ) is T
~ ( ~ P OR Q ) AND ( ~ P OR ~ ( P AND ~ Q ) ) is False

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It is correct.
However note that you could have stopped at "~ ( ~ P OR Q ) is F".
Because is one conjoin is false the whole conjunction is false.

thank you guys !!!