SOLUTION: Given p is true, q is true, and r is false, find the truth value of the statement: ~ p (q v ~r). Please show step by step work, so I can do my other problems.

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p . . . . .q . . . . . r . . . . . ~r . . . . . .~p . . . . . (q v ~r) . . . . . . .~ p n (q v ~r) . . . . . . . ~ p v (q v ~r)
T . . . . . T. . . . .T. . . . . . F. . . . . . . F. . . . . . .T . . . . . . . . . . . . . . . .T. . . . . . . . . . . . . . . .T
T. . . . . F. . . . . T. . . . . . F. . . . . . . F. . . . . . .F . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
T. . . . . T. . . . . F. . . . . . T. . . . . . . F. . . . . . .T . . . . . . . . . . . . . . . .T. . . . . . . . . . . . . . . .T
T. . . . . F. . . . . F.. . . . . . T. . . . . . .F. . . . . . .T . . . . . . . . . . . . . . . .T. . . . . . . . . . . . . . . .T
F. . . . . T. . . . . T. . . . . . F. . . . . . .T. . . . . . .T . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
F. . . . . F. . . . . T. . . . . . F. . . . . . .T. . . . . . .F . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .F
F. . . . . T. . . . . F. . . . . . T. . . . . . .T. . . . . . .T . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
F. . . . . F. . . . . F. . . . . . T. . . . . . .T. . . . . . .T . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
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since I didn't see an operation between ~p and (q v ~r) I did both.

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It depends.

Do you mean



or



If it is the first case, since is true, is false, so false and anything else is false, so the statement is false.

In the second case, is true, is false, so is true and you have true or true which is true. Then is false as before, so you have false or true which is true.

John