Generate test cases for the following code by using logic coverage criteria Statement Coverage. void count (char s[], int &nums, int &letters) { nums= letters =0; for (int i=0;s[i] != '\0'; i++) if(s[i]>= 'A' && s[i]<= 'Z') letters++; else if(s[i]>= 'a'&&s[i]<= 'z') letters++; else if(s[i]>= '0'&&s[i]<='9') nums++ else printf("Not a letter or number!\n"); }

(1) (a) Show that n(n² – 1)(n + 2) is divisible by 4 for all integer n. (b) Prove by contradiction : if n – m is odd , then n2 – m? is odd .

7- Prove that (A+B)(A+C)=A+BC.

Prove each statement using a proof by exhaustion.

Use a software program or a graphing utility to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express X₁, X2, X3, X4, and X5 in terms of the parameter t.) X2 2x3 + 3x4 + 2x5 = 10 X1 + 3X1 + 3х2 - X3 + 2x1 + 2x₂ - X3 + 4x₁ + 4x2 + X3 8x1₁5x22x3 - (X1, X2, X3, X4, X5) = X4 + X5 = 11 X4 - 2x5 = 5 - 3x5 = 11 X4 + 2x5 22

(x^y) → z Solve PV (q^¬q) Solve

Show that 2n  E  O(3n).

Use the Master Theorem to solve the following recurrence equation. DETAILED steps and proofs are required.   T(n) = 9T(n/3)+37n2

6. Prove that if m and n are integers and mn is even, then m is even or n is even.