Free Printable Biconditionals and Definitions

1.

What is the converse of the statement:

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

a)

A number divisible by 20 is even.

b)

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

c)

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

d)

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

2.

What is the truth value of the converse of:

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

a)

True

b)

False

c)

Cannot be determined

3.

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

a)

television

b)

cell phone

c)

computer mouse

d)

keyboard

4.

What is the converse of the statement:

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

a)

2x - 5 = 19

b)

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

c)

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

d)

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

5.

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

a)

True

b)

False

c)

Cannot be determined

6.

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

a)

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

b)

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

c)

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

d)

This statement cannot be written as a true biconditional.

7.

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.

a)

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

b)

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

c)

Not reversible.

8.

Which of the following statements are true biconditionals?

a)

x = 10 if and only if 3x + 2 = 28.

b)

3x + 2 = 11 if and only if x = 3.

c)

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

d)

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

9.

Consider the statement:

If Julie eats tomatoes, then she likes salad.

Is the statement TRUE/FALSE/Cannot be determined?

a)

True

b)

False

c)

Cannot be determined

10.

When can a biconditional statement be true?

a)

When the inverse and the converse are both true

b)

When the original statement (conditional statement) & the contrapositive are both true.

c)

When the converse is true.

d)

When the original statement (conditional statement) and the converse are both true.

11.

Is the statement below a good definition? If not, explain.

A cat is an animal with whiskers.

a)

Good definition

b)

Not good: The statement is not reversible.

c)

Not good: The statement uses vague terms.

d)

Not good: The statement uses terms that are not clearly understood.

12.

Consider the statement:

If points are collinear, then they lie on the same line.

Is the statement TRUE/FALSE/Cannot be determined?

a)

True

b)

False

c)

Cannot be determined

13.

Is the statement below a good definition? If not, explain by checking all reasons that apply.

A segment is part of a line.

a)

Good definition

b)

Not good: The statement is not reversible.

c)

Not good: The statement uses vague terms.

d)

Not good: The statement uses terms that are not clearly understood.

14.

Is the statement below a good definition?

Perpendicular lines are two lines that intersect to form right angles.

a)

Good definition

b)

Not good: The statement is not reversible.

c)

Not good: The statement uses vague terms.

d)

Not good: The statement uses terms that are not clearly understood.

15.

Which conditional and its converse form a true biconditional statement?

a)

$If\ x\ >\ 0,\ then\ \left|x\right|>0.$

b)

$If\ x\ =\ 3,\ then\ x^{2\ }=\ 9.$

c)

$If\ x^3=5,\ then\ x\ =\ 125.\$

d)

$If\ x\ =\ 19,\ then\ 2x\ -\ 3\ =\ 35.\$

16.

What phrase does a biconditional statement use?

a)

if, then

b)

if, when

c)

if and only if

d)

then, if

17.

What is the biconditional that matches the statement: "A right angle is an angle with 90 degrees."

a)

If an angle has 90 degrees, then it is a right angle.

b)

If an angle is a right angle, then it has 90 degrees.

c)

An angle is a right angle if and only if it has 90 degrees.

18.

Is the following a good definition? Elephants are gigantic animals.

a)

Yes

b)

No, because elephants are not gigantic.

c)

No, because it is not written as a biconditional statement.

d)

No, because the converse of the conditional statement is false.

Biconditionals and Definitions

Total questions: 18

Worksheet time: 21mins

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