Question

Write the statement in if-then form in two ways, one of which is the contrapositive of the other: Sam will be allowed on Signe's racing boat only if he is an expert sailor.

Answer 1

1) If Sam is an expert sailor then she will be allowed on Signe's racing boat.

2) If Sam is not allowed on Signe's racing boat, then she is not an expert sailor.

Explanation:

• The contrapositive statement of if P → Q is if ~Q→~P.

In this case we have: If Sam is an expert sailor then she will be allowed on Signe's racing boat.

P = Sam is an expert sailor

Q = Sam will be allowed on Signe's racing boat.

To write the contrapositive statement we're going to say if ~Q→ ~P

If Sam is not allowed on Signe's racing boat, then she is not an expert sailor.