How to solve counterexample problems: meaning, examples, and their solutions.
What is it?
A counterexample is an example
that makes a statement to be false.
Only one counterexample is needed
to prove the statement to be false.
If x = 2,
then p is true (2 is a prime number)
and q is false (2 is not an odd number).
So p → q is false.
Conditional statement: truth value
So the counterexample is x = 2.
If three points are on a same line,
then those three points
cannot determine a triangle.
So it makes the given statement to be false.
So the counterexample is
'three points on a same line'.
To make this statement to be true,
it should be like this:
three non-linear points determine a triangle.