Conditional Statements

Front

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). It is often written in the form "If P, then Q."

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or proposition. It shows that the statement is not always true.

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.

Front

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 true even if the original statement is true.

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 also not necessarily true.

Front

What does it mean if a statement is true?

Back

A statement is true if it accurately reflects reality or a fact.

Tags

CCSS.L.1.1J

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.K.1D

Front

What does it mean if a statement is false?

Back

A statement is false if it does not accurately reflect reality or a fact.

Tags

CCSS.L.1.1J

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.K.1D

Front

Provide an example of a valid counterexample for the statement: 'If it rains, then the ground is wet.'

Back

A valid counterexample would be a situation where it rains but the ground is not wet, such as when the ground is covered.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Front

What is the difference between a hypothesis and a conclusion in a conditional statement?

Back

The hypothesis is the 'if' part of the statement, while the conclusion is the 'then' part. For example, in 'If it is sunny, then I will go outside,' 'it is sunny' is the hypothesis and 'I will go outside' is the conclusion.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Front

What is a logical equivalence?

Back

Two statements are logically equivalent if they have the same truth value in every possible scenario.