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 (p) and a conclusion (q), typically expressed 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 negation of a statement?

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The negation of a statement is the opposite of the original statement. If the original statement is true, the negation is false, and vice versa.

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What is the negation of the hypothesis (~p) in the statement: If it is Valentine's Day, then the month is February?

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It is not Valentine's Day.

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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'.

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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 a biconditional statement?

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A biconditional statement is a statement that combines two conditional statements, expressed as 'p if and only if q', meaning both p and q are true or both are false.

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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 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.