2.3 Biconditionals and Definitions

When a conditional statement and its converse are true, you can combine them as a true __?__.

• hypothesis

• counterexample

• unconditional

• biconditional

A biconditional may be written using the phrase...

• if-then

• if and only if

• not if but then

The converse of the statement p→q is... 

•  $\sim p\rightarrow\sim q$  

•  $p\leftrightarrow q$  

•  $q\rightarrow p$  

•  $\sim q\rightarrow\sim p$  

A biconditional that combines  $p\rightarrow q\ and\ q\rightarrow p$  is ...

•  $\sim p\rightarrow\sim q$  

•  $p\leftrightarrow q$  

•  $q\rightarrow p$  

•  $\sim q\rightarrow\sim p$  

A good definition may be rewritten as a(n) __?__ statement.

• biconditional

• inverse

• contrapositive

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which statement is a counterexample for the following conditional?

If you live in Decatur, then you live in Alabama.

• John Smith lives in Montgomery, Alabama.

• Carson Wilson lives in Hartselle, Alabama.

• Mary Jones lives in Decatur, Georgia.

• Susie Sams lives in Decatur.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

What is the converse of the statement:

"If a number is divisible by 20, then it is even."

• A number divisible by 20 is even.

• If a number is even, then it is divisible by 20.

• If a number is not divisible by 20, then it is not even.

• If a number is not even, then it is not divisible by 20.

What is the truth value of the converse of:

"If a number is divisible by 20, then it is even."

• True

• False

• Cannot be determined

Which is a counterexample for the following conditional:
If an electronic device has a screen then it is a television.

• television
• cell phone
• computer mouse
• keyboard

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

What is the converse of the statement:

"If x = 12, then 2x - 5 = 19"