Conditional Statements

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What is a conditional statement?

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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."

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What is the hypothesis in a conditional statement?

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The hypothesis is the part of the conditional statement that follows 'if'. It represents the condition that must be true for the conclusion to follow.

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What is the conclusion in a conditional statement?

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The conclusion is the part of the conditional statement that follows 'then'. It represents the result that follows if the hypothesis is true.

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What is the contrapositive of a conditional statement?

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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 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'. It is not necessarily logically equivalent to the original statement.

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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'. It is not necessarily logically equivalent to the original statement.

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What is a counterexample?

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

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If the statement is 'If it is a cat, then it is an animal', what is the contrapositive?

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If it is not an animal, then it is not a cat.

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If the statement is 'If it is a square, then it has four sides', what is the inverse?

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If it is not a square, then it does not have four sides.

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What does it mean for two statements to be logically equivalent?

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