Conditional 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 (if part) and a conclusion (then part). It is often written 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 the '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 the 'then'. It represents the result or outcome that follows if the hypothesis is true.

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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." It switches the hypothesis and conclusion.

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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." It negates both the hypothesis and 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." It switches and negates both the hypothesis and conclusion.

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How do you write a conditional statement from a universal statement?

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To write a conditional statement from a universal statement, identify the subject and create a statement in the form "If [subject], then [property]." For example, from "All dolphins are mammals," you can write "If an animal is a dolphin, then it is a mammal."

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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. For example, the negation of "x > 3" is "x ≤ 3."

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What is a biconditional statement?

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A biconditional statement is a statement that combines a conditional statement and its converse, written as "P if and only if Q" (P ↔ Q). It means both P and Q are true or both are false.

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What is an example of a conditional statement in real life?

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An example of a conditional statement is: "If it rains, then the ground will be wet." Here, the hypothesis is 'it rains' and the conclusion is 'the ground will be wet.'