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Logic question

  1. Feb 11, 2013 #1
    [itex]\Rightarrow[/itex]1. The problem statement, all variables and given/known data
    I'm given two statements, p and (q[itex]\Rightarrow[/itex]r) and I need to prove that the two statements are equivalent. So I need to show that p [itex]\Leftrightarrow[/itex](q[itex]\Rightarrow[/itex]r)

    I know that p[itex]\Rightarrow[/itex](q[itex]\Rightarrow[/itex]r) [itex]\Leftrightarrow[/itex] (p[itex]\wedge[/itex]q)[itex]\Rightarrow[/itex]r
    but I don't know how I should rewrite the converse:
    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 11, 2013 #2


    Staff: Mentor

    What if you convert the p --> q to ( not (p and not q) ) and then use Boolean algebra to rework the expression and then convert back.
  4. Feb 11, 2013 #3


    Staff: Mentor

    I think there is some information that is missing here. I don't see how the arbitrary statements p and (q ##\Rightarrow## r) could be equivalent.

    For example, let p, q and r be the following statements:
    p: x = 2
    q: y = 5
    r: y2 = 25

    Whether p is true or false has no bearing on the implication q ##\Rightarrow## r

    Are p, q, and r specific statements that aren't given in the OP?
  5. Feb 11, 2013 #4
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