2.2/2.4: Conditional Statements

Target: Write the inverse, converse, contrapositive, and biconditional of conditional statements.

Statement Definition Example

Conditional

A statement that can be written in the form

“if p, then q”

If an animal is a cat, then it has

four paws.

Hypothesis

Conclusion

Converse

A statement formed by

Inverse

A statement formed by

Contrapositive

A statement formed by

Biconditional

An “if, then” is a conditional statement.

If you switch the if and the then, then it's a converse.

The inverse is a negation: if not p, well then not q.

And the contrapositive combines them: If not q, well then not p.

The biconditional works both ways: p if and only if q

Write the statement as a conditional statement. Then write the related conditional statements below.

Decide if each statement is true by writing True or False next to each statement.

“A straight angle has a measure of 180˚.”

Think and Discuss: What do you notice about the relationships between the truth values

and the different types of statements in regards to definitions?

Conditional Statement

Converse Statement

Inverse Statement

Contrapostive Statement

Biconditional Statement

Is there Logic in Alice in Wonderland? “Then you should say what you mean,” the March Hare went on.

“I do,” Alice hastily replied; “at least – at least I mean what I say – that‟s the same thing, you know.”

”Not the same thing a bit!” said the Hatter, “Why, you might just as well say that

„I see what I eat‟ is the same thing as “I eat what I see‟!”

“You might just as well say,” added the March Hare,

“that „I like what I get‟ is the same thing as „I get what I like‟!”

“You might just as well say,” added the Dormouse, who seemed to be talking in his sleep,

“that „I breathe when I sleep‟ is the same thing as „I sleep when I breathe‟!”

“It is the same thing with you,” said the Hatter.

Let‟s examine two of the statements from their conversation.

Decide if each statement is true by writing True or False next to each statement.

(1) I breathe when I sleep. (2) I sleep when I breathe.

Write each of these statements as conditional statements.

(1) If I breathe, then I sleep. (2)

Write the converse of each statement.

(1) (2)

Write the inverse of each statement.

(1) (2)

Write the contrapositive of each statement.

(1) (2)

Write the biconditional of each statement.

(1) (2)

Think and Discuss: What do you notice about the relationships between the truth value and

the different types of statements if it is not a definition? (Write one to two sentences.)