Conditional, Converse, Counterexample Review

Front

What is a conditional statement?

Back

A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). For example, 'If it rains, then the ground is wet.'

Front

What is the converse of a conditional statement?

Back

The converse of a conditional statement 'If p, then q' is 'If q, then p'. For example, the converse of 'If it rains, then the ground is wet' is 'If the ground is wet, then it rains.'

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or conjecture. It shows that the statement is not always true.

Front

Given the conditional 'If Jose eats fish, then he has an allergic reaction', what is the converse?

Back

If Jose has an allergic reaction, then he ate fish.

Front

Given the conditional 'If it is a duck then it has a beak', what is the converse?

Back

If it has a beak, then it is a duck.

Front

What is the converse of the statement 'If you are 13, then you are a teenager'?

Back

If you are a teenager, then you are 13.

Front

How can you prove a conjecture is false?

Back

By providing a counterexample.

Front

If an animal is furry, then it is a hamster. What would be an appropriate counterexample?

Back

A cat.

Front

What is the hypothesis in a conditional statement?

Back

The hypothesis is the 'if' part of a conditional statement. It is the condition that must be met.

Front

What is the conclusion in a conditional statement?

Back

The conclusion is the 'then' part of a conditional statement. It is the result that follows if the hypothesis is true.