Conditional Statements

Front

What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, where one proposition (the hypothesis) implies the other (the conclusion).

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What is the converse of a conditional statement?

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The converse of a conditional statement 'If P, then Q' is 'If Q, then P.'

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What is the inverse of a conditional statement?

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The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q.'

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.'

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What is a counterexample?

Back

A counterexample is an example that disproves a conjecture or statement.

Front

If a statement is true, what can be said about its contrapositive?

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The contrapositive of a true statement is also true.

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If a statement is false, what can be said about its converse?

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The converse of a false statement can be either true or false; it is not guaranteed to be false.

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What is the negation of a statement?

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The negation of a statement is the opposite of the statement, indicating that the statement is not true.

Front

What is the relationship between a statement and its inverse?

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A statement and its inverse can both be true or both be false; they are not logically equivalent.

Front

Provide an example of a conditional statement.

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If it rains, then the ground will be wet.