Conditional Statements

2-2 Conditional Statements

page 89

9/18/20

Objectives

Objectives

• To recognize conditional statements and their parts

• To write converses, inverses, and contrapositives.

• A conditional is an if-then statement.

• The hypothesis is the part p following if.

• The conclusion is the part q following then.

Multiple Choice

What is the converse to this statement?

If it is dark outside, then it is night.

• If it isn't dark outside, then it is not night.

• If it is not night, then it is not dark outside.

• If it is night, then it is dark outside.

• It is night.

Multiple Choice

What is the inverse to this statement?

If you live in Montreal, then you live in Canada.

• If you live in Canada, then you live in Montreal

• If you don't live in Montreal, then you don't live in Canada.

• If you don't live in Canada, you don't live in Montreal.

• Montreal is in Brazil.

Symbols

 $p\rightarrow q$ 

 reads as      "if p then q"
                                  or       
                     "p implies q"

problem 1

If an animal is a robin, then the animal is a bird.

hypothesis (p): An animal is a robin

Conclusion (q): The animal is a bird.

Writing a Conditional

Vertical angles share a vertex.

If two angles are vertical, then they share the vertex.

Problem 2 Got it?

Dolphins are mammals.

?????

Multiple Choice

What is the hypothesis in the conditional

If an angle measures 130, then the angle is obtuse.

• An angle measures 130.

• The angle is obtuse.

The truth value of a conditional is either true or false. 

To show that a conditional is true, show that everytime the hypothesis is true, the conclusion is also true. A counterexample can help you determine whether a conditional with a true hypothesis is true. To show that the conditional is false, if you find one counterexample for which the hypothesis is true and the conclusion is false, then the value of the conditional is false.

The negation of a statement p is the opposite of a statement

The symbol is ~p and is read "not p"

ex) The negation to the statement "The sky is blue" is "The sky is not blue"

You can use negations to write statements related to a conditional.

Every conditional has three related conditional statements.

Multiple Choice

What is the converse to this statement?

If it is dark outside, then it is night.

• If it isn't dark outside, then it is not night.

• If it is night, then it is dark outside.

• If it is not night, then it is not dark outside.

• It is night.

Multiple Choice

What is the inverse to this statement?

If you live in Montreal, then you live in Canada.

• If you live in Canada, then you live in Montreal.

• If you don't live in Montreal, then you don't live in Canada.

• If you don't live in Canada, you don't live in Montreal.

• Montreal is in Brazil.

Multiple Choice

 $\sim q\rightarrow\sim p$  
What does this mean?

• Conditional Statement

• Inverse

• Converse

• Contrapositive

Multiple Choice

 $\sim q\rightarrow\sim p$  
What does this mean?

• Conditional Statement

• Inverse

• Converse

• Contrapositive