This is discrete math subject please write clealy and solve question 5 please 1.

Question

This is discrete math subject please write clealy and solve question 5 please

1. Prove that, for all n23, 6">40+90 2. Let f:Z ->Z and g:Z ->Z be given by f(n)-n+10 and g(n)-2n1 +1- (a) Are f and/or g injective (b) Are f and/or g surjective (c) Is either map invertible 2 3. Construct, if possible, a 1-1 correspondence between the following sets or explain why no such map exists: (a) the power set P(A) of the set A (1 , 2 } and the set {n Z | 1 n2 ) the real numbers R and the set of polynomials of degree

Explanation / Answer

Ans 5.

(a) f(n) = 1 + 2 + 3 + 4 + n(n+1) = n(n+1)[n(n+1) + 1]/2 = (1/2)*(n^4 + 2n^3 + 2n^2 + n)

=> f(n) has O(n^4)

(b) f(n) = 10^n + n^10 + n!

since at a very lareg value of n, n! will majorly govern the value of f(n)

f(n) has O(n!)

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