# Taking the contrapositive of this statement?

1. Apr 25, 2013

### bonfire09

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. Apr 25, 2013

### yossell

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',

3. Apr 25, 2013

### Fredrik

Staff Emeritus
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).