Applications of Discrete Mathematics

Complete the following in a 1-page paper:

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.