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 the form 'If P, then Q', where P is the hypothesis and Q is the 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'.

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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 does 'biconditional' mean?

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A biconditional statement is a statement that contains the phrase 'if and only if', indicating that both conditions are equivalent.

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How do you write a biconditional statement?

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A biconditional statement can be written as 'P if and only if Q', meaning P is true when Q is true and vice versa.

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What is an example of a biconditional statement?

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An example of a biconditional statement is 'A triangle is equilateral if and only if all its sides are equal.'

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What is the relationship between a conditional statement and its contrapositive?

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A conditional 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 conditional statement and its converse?

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

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What is the relationship between a conditional statement and its inverse?

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