Conditional Statements

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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). It is often written in the form 'If p, then q'.

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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 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 switches the hypothesis and conclusion.

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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 negates both the hypothesis and conclusion.

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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 switches and negates both the hypothesis and conclusion.

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If angles are congruent, then the measures of the angles are equal. What is the contrapositive?

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If the measures of the angles are not equal, then the angles are not congruent.

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If it is a triangle, then it has three sides. What is the inverse?

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If it is not a triangle, then it does not have three sides.

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What does 'p → q' represent in logic?

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'p → q' represents a conditional statement where 'p' is the hypothesis and 'q' is the conclusion.

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What is the relationship between a statement and its contrapositive?

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