Let A = {(N1, N2) | N1 and N2 are NFAS and L(N1)N L(N2) = Ø}. Show that A is %3D decidable.

Formally prove or disprove the following claimssnip

Prave that if 3nt4 is then odd.

Prove that if n is a positive integer, then n is even if andonly if 7n + 4 is even. Prove that m2= n2if and only if m = n or m = −n.

1. Prove the following 100n +5 = O(n) 1000n? +100n -6 = O(n²)

Find the value of x for the following sets of congruence using the Chinese remainder theorem.a. x ≡ 2 mod 7, and x ≡ 3 mod 9b. x ≡ 4 mod 5, and x ≡ 10 mod 11c. x ≡ 7 mod 13, and x ≡ 11 mod 12

7. Prove that if 7 divides n with remainder 1, 7 divides n² + 2n +7 with remainder 3.

Let A = {m ∈ Z | m ≡ 9 (mod 12)}. Let B = {n ∈ Z | n ≡ 1 (mod 4)}.

Given the following recurrence, find the growth rate of T(n):T(n) = 4T(n/2) + 6n3 with T(1) = Θ(1)

Use strong induction to prove the following: