Conditional Statements & Related Conditionals

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What is a conditional statement?

Back

A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). For example, 'If it rains, then the ground is wet.'

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P.' It is logically equivalent to the original statement.

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What is the converse of a conditional statement?

Back

The converse of a conditional statement 'If P, then Q' is 'If Q, then P.' It is not necessarily logically equivalent to the original statement.

Front

What is the inverse of a conditional statement?

Back

The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q.' It is not necessarily logically equivalent to the original statement.

Front

What is an acute angle?

Back

An acute angle is an angle that measures less than 90 degrees.

Tags

CCSS.4.G.A.1

Front

What is a triangle with 3 congruent sides called?

Back

A triangle with 3 congruent sides is called an equilateral triangle.

Tags

CCSS.4.G.A.2

Front

What is the truth value of a conditional statement?

Back

The truth value of a conditional statement indicates whether the statement is true or false based on the truth of its hypothesis and conclusion.

Front

Provide an example of a counterexample for a conditional statement.

Back

For the statement 'If an angle is acute, then it measures 30 degrees,' a counterexample is an angle measuring 20 degrees, which is acute but does not measure 30 degrees.

Front

What does it mean if a conditional statement is false?

Back

A conditional statement is false if the hypothesis is true and the conclusion is false.

Front

What is the relationship between a conditional statement and its contrapositive?

Back

A conditional statement and its contrapositive are logically equivalent; if one is true, the other is also true.