Biconditionals and Definitions

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.

Tags

CCSS.HSS.CP.A.1

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

What is the converse of the statement:

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

• 2x - 5 = 19

• $If\ x\ne12,\ then\ 2x\ -\ 5\ \ne19$

• $If\ 2x\ -\ 5\ =\ 19,\ then\ x\ =\ 12.$

• $If\ 2x\ -\ 5\ \ne\ 19,\ then\ x\ \ne12.$

What is the truth value of the statement,  $If\ 2x\ -\ 5\ =\ 19,\ then\ x\ =\ 12.$  

• True

• False

• Cannot be determined

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Write the true biconditional for the statement:  $If\ x\ =\ 12,\ then\ 2x\ -\ 5\ =\ 19.\$  

•  $If\ 2x\ -\ 5\ =\ 19,\ then\ x\ =\ 12.\$  

•  $x\ =\ 12\ if\ and\ only\ if\ 2x\ -\ 5\ =\ 19.\$  

•  $x\ =\ 12\ and\ 2x\ -\ 5\ =\ 19.\$  

• This statement cannot be written as a true biconditional. 

Test the statement below to see if it is reversible. If so, write it as a biconditional.

Complementary angles are two angles with measures that have a sum of 90.

• Reversible; If two angles are complementary, then the sum of their measures is 90.

• Reversible; Two angles are complementary if and only if the sum of their measures is 90.

• Not reversible.

Tags

CCSS.HSG.CO.A.1

Which of the following statements are true biconditionals?

• x = 10 if and only if 3x + 2 = 28.

• 3x + 2 = 11 if and only if x = 3.

• $x^{2\ }=\ 25\ if\ and\ only\ if\ x\ =\ -5.$

• $x^3=125\ if\ and\ only\ if\ x\ =\ 5.$

Consider the statement:

If Julie eats tomatoes, then she likes salad.

Is the statement TRUE/FALSE/Cannot be determined?

• True

• False

• Cannot be determined

When can a biconditional statement be true?

• When the inverse and the converse are both true
• When the original statement (conditional statement) & the contrapositive are both true.
• When the converse is true.
• When the original statement (conditional statement) and the converse are both true.