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) + q3. Design the combinatorial circuit for: [(p q ) V ( r V q)] s4. Complete the truth table of the following Boolean expression: p (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: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.Inputm= mustard button (1 = pushed 0 = not pushed)k= ketchup button (1 = pushed 0 = not pushed)r= relish button (1 = pushed 0 = not pushed)OutputHot dog that satisfies the constrains.

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