A) Prove with Boolean algebra that:(x + y) * (x’ + y) = yGive a reason for each step in your proof. B) Show the dual proof of part (A).

I'm not sure how to use pumping lemma on this or if I should be using a different method

Let ƒ : Z → Z be some function over the integers. Select an appro- priate proof technique (direct, contradiction, induction, invariant or pigeonhole), and prove that if you have: a, f(a), ƒ(f(a)), ƒ(f(f(a))) and f(f(f(f(@)))), then at least 2 of those numbers are equivalent modulo 4.

I need the answer as soon as possible

Answer the following questions: a. Apply DeMorgan's Theorems to the following expression F = (ABC + DEF)' b. Apply DeMorgan's Theorems to the following expression F = ((A+B+C). D)' c. Use DeMorgan's Theorem in algebraic form to Prove F = A' + B' (A. B)' d. Use DeMorgan's Theorem in algebraic form to Prove F = A'. B' = (A + B)' e. Minimize the following Logic Expressions F, Y Algebraically and PROVE the function F to be equal to A'.C' + B, and the function Y to be equal to A+BC. A'.B'.C + A'.B.C'+A'.B.C+A.B.C'+A.B.C F (A, B, C) Y (A, B, C) (A+B) (A+C)

Sam thinks that AB + A'B' simplifies to 1 by the Inverse law. a. Using the DeMorgan and Involution laws, express the inverse of A'B' as a boolean expression bexp5d that is a sum of literals. Show the application(s) of each law. b. Using the DeMorgan and Involution laws, express the inverse of (A'+B+C') as a boolean expression bexp5e that is a product of literals. Show the application(s) of each law.

Can you represent the following Boolean function f(A, B) with a linear classifier? If yes, show the linear classifier. If not, briefly explain why not. f(A, B) A B 1 1 1 1

Use the pumping lemma to prove the following language is nonregular:L = {anb3n} = {abbb, aabbbbbb, aaabbbbbbbbb, …}

9. Given the following Boolean Function: F(A, B, C) = AB+B(Ā+C) Determine the canonical form for the SOP (sum of minterms) and POS (product of maxterms). Also, draw the truth tables showing the minterms and maxterms.

2. (a) Compute and simplify f = (xz+ (y+t)' + (xz)'y')' Encircle final answer! (b) Prove or disprove that in any Boolean algebra, B: (i) 0' = 1 (ii) 1' = 0