Mathematical Proofs: Introduction and Basic Techniques
This worksheet introduces fundamental concepts and techniques in mathematical proofs, suitable for Grade 10 students.
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Mathematical Proofs: Introduction and Basic Techniques
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following is a statement that has been proven to be true?
Conjecture
Axiom
Theorem
Hypothesis
2. A mathematical proof is a argument that demonstrates a statement is true.
3. The starting points of a proof, which are accepted without proof, are called .
4. A counterexample is sufficient to prove a statement true.
True
False
5. State the Law of Detachment.
6. Prove the following statement using a direct proof:
If n is an even integer, then n² is an even integer.
7. Prove the following statement using proof by contrapositive:
If n² is an odd integer, then n is an odd integer.
8. Consider the statement: "If it is raining, then the ground is wet."
a) Write the converse of the statement.
b) Write the inverse of the statement.
c) Write the contrapositive of the statement.