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6. For each integer n ≥ 0, 5n - 1
4
6
14
3
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7. While proving the inductive step, how many times is the inductive hy- pothesis used?
Sometimes, never used
More than once
Once, only if it is proved to be true.
Cannot say
8. By the principle of mathematical induction, Σni=0 P(i) = n2(n + 1). For what choice of P (i) will induction work?
3i2 - 2
i2 - 2
3i2 - 1
3i2 - i
9. Let f : X → Y be a function such that |X| > |Y |, then by Pigeonhole Principle, we can conclude that
f is not one-one
f is not onto
f is one-one
f is onto
10. Let P(n) : n2 < 2n. Then basis step is
n = 4
n = 6
n = 5
n = 3
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