Contrapositivity question (1 Viewer)

[AbstractBlade]

Question 15. If ab is divisible by 3, prove by contrapositive that a or b is divisible by 3.

 

[tito981]

therefore, rtp: both a,b are not divisible by 3 , then ab is not divisible by 3.
then take cases
1: a=3p+1, b=3q+1
2: a=3p+2, b=3q+1
3: a=3p+2, b=3q+2
and prove that ab is not divisible by 3.
then re-state the question and say by contrapositive must be true.
(idk specifically for this question if you have to take cases, but i would in case you are required to)

 

[CM_Tutor]

This is an example where taking cases is made much easier by modulo arithmetic