Q2 of 27 Page 4

Write the set of value of n for which the statement P(n): 2n<n! is true.


For n = 1


2(1) ≮ 1!


For n = 2


2(2) ≮2!


4 ≮2


For n = 3


2(3) ≮3!


6 ≮6


For n = 4


2(4) < 4!


8 < (4× 3× 2× 1)


8 < 24


Hence for n ⩾ 4 the statement is true.


∴ The solution set is {n ∈ N: n ⩾ 4}.


More from this chapter

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Let P(n): n2 >9. Is P (2) true?

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If P(n) is the statement “n (n + 1) is even”, then what is P(4)?