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Questions and Answers
Which of the following best describes the concept of a tautology in mathematical reasoning?
Which of the following best describes the concept of a tautology in mathematical reasoning?
- A statement that is sometimes false, depending on the truth values of its components
- A statement that is always true, regardless of the truth values of its components (correct)
- A statement that is sometimes true, depending on the truth values of its components
- A statement that is always false, regardless of the truth values of its components
What is the contrapositive of the statement 'If a number is divisible by 3, then it is divisible by 6' in mathematical reasoning?
What is the contrapositive of the statement 'If a number is divisible by 3, then it is divisible by 6' in mathematical reasoning?
- If a number is divisible by 6, then it is divisible by 3
- If a number is not divisible by 6, then it is not divisible by 3
- If a number is divisible by 6, then it is not divisible by 3
- If a number is not divisible by 3, then it is not divisible by 6 (correct)
What is the negation of the statement 'If it is raining, then the ground is wet' in mathematical reasoning?
What is the negation of the statement 'If it is raining, then the ground is wet' in mathematical reasoning?
- It is not raining and the ground is not wet
- It is raining and the ground is wet
- It is raining and the ground is not wet
- It is not raining and the ground is wet (correct)
