IM2 Section 1-4 to 1-7 Review

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

• 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.

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.

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.

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

A cat is an animal with whiskers.

• Good definition

• Not good: The statement is not reversible.

• Not good: The statement uses vague terms.

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

What phrase does a biconditional statement use?

• if, then
• if, when
• if and only if
• then, if

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

• If an angle has 90 degrees, then it is a right angle.
• If an angle is a right angle, then it has 90 degrees.
• An angle is a right angle if and only if it has 90 degrees.