Appendix 1: Proofs in Mathematics — Practice Quiz
Madhya Pradesh Board · Class 12 · Mathematics
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Which option gives the correct factorization of x^2 - 5x + 6 used in a direct proof example?
In a proof, what is the meaning of a statement being justified by definitions, axioms, or previously established propositions?
Which condition is the defining property of a one-one function?
Which expression is the contrapositive of p ⇒ q?
Sample Questions
Which method proves a statement by assuming it is false and then reaching a contradiction?
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Proof by contradiction
Proof by contradiction starts with the false assumption of the statement and derives a contradiction.
Which of the following best describes the principle of mathematical induction?
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If the base case is true and k implies k+1, then the statement is true for all n from the starting point onward
Mathematical induction uses a true starting case and a true inductive step to conclude truth for all later natural numbers.
Which number is constructed in the proof that the set of primes is infinite?
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N = (P1P2P3...Pk) + 1
The constructed number is the product of the assumed finite list of primes plus 1.
Which statement is true about the function φ(x) = |x|?
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It is continuous everywhere but not differentiable at x = 0
The absolute value function is continuous for all x, but it fails to be differentiable at x = 0.
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