Which of the following is the contrapositive of “If three points lie on the same line, then they are collinea

Question

If three points do not lie on the same line, then they are not collinear.

If three points are collinear, then they lie on the same line.

If three points are collinear, then they are coplanar.

If three points are not collinear, then they do not lie on the same line.

Answer 1

The contrapositive of "If P, then Q" is "If not Q, then not P". So the contrapositive here is "If three points are not collinear, then they do not lie on the same line." So the last statement is the contrapositive.

By the way, as for the other answers: the first is the inverse. The second is the converse. The third is some completely different statement about lines being coplanar.

Answer 2

statement
A implies B

contrapositive = not B implies not A
A = if three points lie on the same line
B = they are co-linear.

not B = if they are not co-linear,
then
not A = the three points do not lie on the same line.


The inverse is:
not A implies not B (not always true; in this case it is true)

The converse is
B implies A (not always true, but in this case it would be, because it is a statement of equivalence, not just one of implication).

The contradiction, if there were one, would be:
A, yet not B (does not exist in this case)
It would be written
We have three points on the same line, yet they are not co-linear.

Answer 3

1st one