Science:Math Exam Resources/Courses/MATH220/December 2011/Question 02 (b)/Solution 1

• The statement

$\displaystyle P(3)\Rightarrow Q(4)$

is "3 is divisible by 4 implies that 17 is divisible by 3".

• The converse is

$\displaystyle Q(4)\Rightarrow P(3)$

hence in words it is "17 is divisible by 3 implies that 3 is divisible by 4".

• The contrapositive is

$\displaystyle \lnot Q(4)\Rightarrow \lnot P(3)$

In words this is "17 is not divisible by 3 implies that 3 is not divisible by 4".