**Indirect Proof.**Give an indirect proof for the following claim:If

*m*and*n*are odd integers, then*m*⋅*n*is an odd integer.

**Proof by Contradiction.**Prove by contradiction that the following graph is not 3-colorable.

**Proof by Cases.**[Adapted from Rosen 5/e.]

Let min:**R**×**R**→**R**be the function that "returns" the minimum of two values. (Here,**R**is the set of real numbers.)For example,

min(3.1, 5) = 3.1

min(17.2, 9.4) = 9.4Prove by cases, that for all real numbers

*a*,*b*and*c*, thatmin(min(

*a*,*b*),*c*) = min(*a*, min(*b*,*c*))

Last Modified: 25 Feb 2016 21:44:48 EST by Richard Chang to Spring 2016 CMSC 203-06 Homepage