LO 5: Conditional Statements (3)

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). It is often written in the form 'If P, then Q'.

Front

In the statement 'If you are in California, then you are in Los Angeles', what is the hypothesis?

Back

The hypothesis is 'you are in California'.

Front

In the statement 'If a man speaks two languages, then he is bilingual', is the statement true or false?

Back

True.

Front

What is the conclusion in the statement 'If you are in California, then you are in Los Angeles'?

Back

The conclusion is 'you are in Los Angeles'.

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'.

Front

What is the converse of the statement 'If a whole number ends in 8, then it is divisible by 2'?

Back

The converse is 'If a whole number is divisible by 2, then it ends in 8'.

Front

Is the converse of the statement 'If you are in Los Angeles County, then you are in Pacoima' true or false?

Back

False.

Front

What does it mean for a conditional statement to be true?

Back

A conditional statement is true unless the hypothesis is true and the conclusion is false.

Front

What is an example of a false conditional statement?

Back

An example is 'If it is raining, then the ground is dry.' This is false because it is possible for it to be raining and the ground to be wet.

Front

What is the relationship between a conditional statement and its contrapositive?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P', and it is logically equivalent to the original statement.