3. (1 pt) Simplify the Boolean function using K-map. AB 00 01 11 10 1 1 1 1

3- Apply De Morgan's theorem to :- A.B + A.B =

7. (a) Prove with Boolean algebra that (x + y) + (y · x') = x + y. Give a reason for each step in your proof. (b) Show the dual proof of part (a).

4. Using DeMorgan's theorem simplify the following expression: (a'+ bc')'

Prove the following three identity laws by showing the corresponding truth tables for both AND form and OR form: 1) Distributive Law2) Absorption Law3)DeMorgan's Law

Provide the Boolean expression for X and simplify it. A O BO

6. (a) Prove with Boolean algebra that (x + y) (x' + y) = y. Give a reason for each step in your proof. (b) Show the dual proof of part (a).

1. For each sequence given below, find a closed formula an for the nth term of the sequence (assume the first terms are ao) by relating it to another sequence for which you already know the formula. (a) 4, 5, 7, 11, 19, 35, ... (b) 0, 3, 8, 15, 24, 35, ... . . (c) 6, 12, 20, 30, 42, ... (d) 0, 2, 7, 15, 26, 40, 57, ... (Hint: These might be called "house" numbers, as in "house of cards")

can someone help me please and solve this questions with steps please

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

2.a Convert both combinational circuits in a. and b. to Booleans functions with applying K-map on extracted terms to get the optimized versions of both of them. A=D एज a. A-