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.

Algebra ->  Conjunction -> 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.      Log On


   

Question 261274: 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.
Found 2 solutions by drk, solver91311:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
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.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


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