No. 2 please.

Prove x + ~xy = x + y using direct applications of Boolean Algebra laws and truth tables. Simplify the following Boolean expressions using Karnaugh maps: a. A bar B CD bar + A bar B C bar D + ABCD bar + AB C bar D b. ABCD bar +AB bar C D bar + A BCD bar +A B bar C D bar c. ABCDE bar +ABCD bar E + AB bar C D bar E + AB bar C DE bar + A bar B CDE bar + A bar B CD bar E + A bar BC D bar E + A bar BC DE bar d. A + AB CD bar + A B bar C D bar Derive a Boolean expression for a voting machine which allows three persons to vote The output is either yes or no dependent on the number of persons voting yes. Two restrictions: 1) No abstain allowed. That is each person has to vote either yes or no. 2) The outcome is yes if two or more yes votes: otherwise, the outcome is no. Normally when forming a voting group, like board of trustee, the number of voting members is designated to an odd number to avoid a tie situation. Derive a sum-of-product format first and then use Karnaugh maps to simplify the expression. An equivalent circuit for an AND gate is shown below