Introduction to Mathematical Proofs
This worksheet introduces grade 11 students to fundamental concepts and techniques in mathematical proofs, including direct proof, proof by contradiction, and propositional logic.
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Introduction to Mathematical Proofs
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Carefully read each question and follow the instructions. Show all your work for proofs.
1. A statement that can be either true or false, but not both, is called a .
2. The negation of a statement P is denoted by and has the opposite truth value of P.
3. A compound statement using the word 'and' is called a .
4. A compound statement using the word 'or' is called a .
5. Which of the following is a proposition?
What time is it?
x + 2 = 5
The sky is blue.
Go clean your room!
6. Prove the following statement using a direct proof: If n is an even integer, then n + 3 is an odd integer.
7. Prove by contradiction: If 3n + 2 is odd, then n is odd.
8. The statement "All squares are rectangles" is true.
True
False
9. The negation of "It is raining" is "It is not raining."
True
False
10. Prove that the sum of two odd integers is always an even integer.