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Taking the contrapositive of this statement?

  1. Apr 25, 2013 #1
    Statement: If every right triangle has angle defect equal to zero then the angle defect of every triangle is equal to zero

    Taking the contrapositive do i have this correct? : There exists at least one triangle whose angle defect is not zero such that not every right triangle has an angle defect equal to zero.
  2. jcsd
  3. Apr 25, 2013 #2
    The contrapositive of a conditional is another conditional. But there appears to be no conditional in your version - instead, you've a 'such that'. 'if' at the front and 'then' for 'such that',
  4. Apr 25, 2013 #3


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    R = the set of all right triangles
    T = the set set of triangles
    Z = the set of all triangles with angle defect zero

    If (for all x in R, x is in Z), then (for all x in T, x is in Z).

    The contrapositive of ##p\Rightarrow q## is ##\lnot q\Rightarrow\lnot p##, so the contrapositive of the implication above is

    If (there exists an x in T such that x is not in Z), then (there exists an x in R such that x is not in Z).
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