# Taking the contrapositive of this statement?

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.

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yossell
Gold Member
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',

Fredrik
Staff Emeritus
Gold Member
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).