# 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 ->  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

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 Logic: Propositions, Conjunction, Disjunction, Implication Solvers Lessons Answers archive Quiz In Depth

 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)   (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 --- since I didn't see an operation between ~p and (q v ~r) I did both. Answer by solver91311(16868)   (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