Conditional Statements

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What is a Conditional Statement?

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A statement that can be written in the form 'If p, then q', where p is the hypothesis and q is the conclusion.

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What is the hypothesis in a Conditional Statement?

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The part of the statement that follows 'if'. For example, in 'If it rains, then I will stay home', the hypothesis is 'it rains'.

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What is the conclusion in a Conditional Statement?

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The part of the statement that follows 'then'. For example, in 'If it rains, then I will stay home', the conclusion is 'I will stay home'.

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What is the Inverse of a Conditional Statement?

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The statement formed by negating both the hypothesis and the conclusion. For example, the inverse of 'If p, then q' is 'If not p, then not q'.

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What is the Converse of a Conditional Statement?

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The statement formed by switching the hypothesis and conclusion. For example, the converse of 'If p, then q' is 'If q, then p'.

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What is the Contrapositive of a Conditional Statement?

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The statement formed by negating both the hypothesis and conclusion and switching them. For example, the contrapositive of 'If p, then q' is 'If not q, then not p'.

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What does the symbol '~' represent in logic?

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The symbol '~' represents negation. For example, if p is true, then ~p is false.

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What is the truth value of a Conditional Statement?

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A conditional statement is false only when the hypothesis is true and the conclusion is false.

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What is a Tautology in logic?

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A statement that is always true, regardless of the truth values of its components.

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What is a Contradiction in logic?

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A statement that is always false, regardless of the truth values of its components.