Logical Reasoning Flashcard

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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 (if part) and a conclusion (then part). For example, 'If it rains, then the ground is wet.'

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What is the hypothesis in a conditional statement?

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The hypothesis is the 'if' part of a conditional statement. It represents the condition that must be met for the conclusion to be true.

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What is the conclusion in a conditional statement?

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The conclusion is the 'then' part of a conditional statement. It represents the result or outcome that follows from the hypothesis.

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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 an 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 is not 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 and is true if both parts are true. It is often expressed as 'p if and only if q'.

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How do you identify the hypothesis and conclusion in a statement?

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In a statement of the form 'If p, then q', 'p' is the hypothesis and 'q' is the conclusion.

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

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A conditional statement and its contrapositive are logically equivalent, meaning they have the same truth value. However, they are expressed differently.

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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; they can have different truth values.

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Provide an example of a conditional statement.

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Example: 'If a shape is a square, then it has four equal sides.'