1.5 Conditional and Biconditional 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 (p) and a conclusion (q), typically expressed in the form "If p, then q."

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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."

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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."

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What does 'negation' mean in logic?

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Negation is the logical operation that takes a statement and flips its truth value. For example, the negation of 'p' is 'not p'.

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What is a biconditional statement?

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A biconditional statement is a logical statement that combines a conditional statement and its converse, expressed as "p if and only if q" (p ↔ q).

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How do you form the contrapositive of a statement?

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To form the contrapositive, negate both the hypothesis and conclusion of the original statement and reverse their order.

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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.

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What is the relationship between a statement and its inverse?

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A statement and its inverse are not logically equivalent; one can be true while the other is false.

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What is the relationship between a statement and its converse?

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A statement and its converse are not logically equivalent; one can be true while the other is false.