1. Simplify the following Boolean expression: AB(A + B)(C + C)
2. Design the combinatorial circuit for: (p' *r) + q
3. Design the combinatorial circuit for: [(p Λ q') V ( r V q)] Λ s
4. Complete the truth table of the following Boolean expression: p' Λ (q V r )
5. Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for your proof or complete the two truth tables:
(A + C)(AD + AD') + AC + C
A + C
6. The AIU cafeteria wants to provide an electronic hot dog machine. Design the machine so that it accepts 3 choices, it has a button for each choice, and a customer can select no more than 2 of the 3 choices. Design a circuit to ensure that the above conditions are satisfied.
Input
m = mustard button (1 = pushed, 0 = not pushed)
k = ketchup button (1 = pushed, 0 = not pushed)
r = relish button (1 = pushed, 0 = not pushed)
Output
Hot dog that satisfies the constrains.