Discrete Maths - Combinatorics

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6. For each integer n ≥ 0, 5ⁿ - 1

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Option : A
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7. While proving the inductive step, how many times is the inductive hy- pothesis used?

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Option : C
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8. By the principle of mathematical induction, Σⁿ_i=0 P(i) = n²(n + 1). For what choice of P (i) will induction work?

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Option : D
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9. Let f : X → Y be a function such that |X| > |Y |, then by Pigeonhole Principle, we can conclude that

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Option : A
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10. Let P(n) : n² < 2ⁿ. Then basis step is

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Option : C
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