Chapter 2 Review

p → q

• conditional statement

• converse
• inverse 
• contrapositive

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

q → p

• conditional statement

• converse
• inverse
• contrapositive

~p → ~q

• conditional statement

• converse
• inverse
• contrapositive

What is the inverse to this statement?

• If you live in Canada, 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.

What is the converse to this statement?

• 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.

~q → ~p

• conditional statement

• converse
• inverse
• contrapositive

What is the contrapositive to this?

• If the food is not cooked, then it is not in the oven.
• If the food is not in the oven, then it is not cooked.
• If the food is cooked, then it is in the oven.

• If food is not in the oven, then it is cooked.

TRUE or FALSE?

"If an angle is acute, then it measures 30 degrees."

• TRUE.

  All acute angles measure 30 degrees.

• FALSE.

  An angle can be acute and not measure 30 degrees.

  Counterexample: An angle measuring 20 degrees is acute and does not measure 30 degrees.

• FALSE.

  Some 30-degree angles are acute, while other 30-degree angles are obtuse.

• Not enough information to determine the truth value for the given conditional statement.

Tags

CCSS.HSG.CO.A.1

Consider the conditional statement "If today is Saturday, then it's the weekend".

Identify the converse statement and whether it's TRUE or FALSE.

[Hint: The converse of "If p, then q" is "If q, then p".]

• The converse is "If today is not Saturday, then it's not the weekend."

  This is TRUE.

• The converse is "If today is not Saturday, then it's not the weekend."

  This is FALSE because it could be Sunday.

• The converse is "If it's the weekend, then today is Saturday."

  This is FALSE because it could be Sunday.

• The converse is "If it's not the weekend, then today is not Saturday."

  This is TRUE.

Which is a counterexample of: If a four sided shape has two sides the same length, then it must be a rectangle.

• quadrilateral
• rectangle
• square
• triangle

Tags

CCSS.HSG.CO.C.11