Math 271 Homework due 11.59pm Sept 28 Instructions: Write down complete solutions to the following problems. Upload your solutions to D2L by 11.59pm on September 28. 1. Find the Boolean expression for the circuit below. 2. Find the Boolean expression for the following circuit. 2. Find the Boolean expression for the following circuit. 11 ac 4. Design a circuit using only AND and NOT gates that realizes this truth table (you have to use DeMorgan's Laws to convert any ORs you get to ANDs and NOTs). Minimize the number of gates you have to use. X1 X2 output 0 0 0 0 1 1 1 0 1 1 5. Design a circuit using only AND and NOT gates that realizes this truth table (you have to use DeMorgan's Laws to convert any ORs you get to ANDs and NOTs). Minimize the number of gates you have to use. X1 X2 output 0 0 1 0 1 1 1 0 0 1 1 1 6. Let U = {1,2,3,4,5,6,7,8,9,10), and let A = {1,4,7,10), B = {1,2,3,4,5), and C = {2,4,6,8). List the elements of An (BUC). 7. Let U = {1,2,3,4,5,6,7,8,9,10). Let A = {1,4,7,10), B = {1,2,3,4,5), and C = {2,4,6,8).. List the elements in the set (ANB)-C. 8. Let U = {1,2,3,4,5,6,7,8,9,10). Let A = {1,4,7,10); B = {1,2,3,4,5); C = {2,4,6,8). List the elements in the set Bn (C - A). 9. Draw a Venn diagram with three sets and shade the set B n (C - A). 10 a. Use a Venn diagram to show that AU (BNC) = (AUB) N (AUC). b. Use a truth table to show that p V (qar) = (p V9) A (p Vr). c. Use Boolean algebra to show that x1 + (x2 * x3) = (x1 + x2). (X1 + x3). d. Explain the connections between 10a, 10b, and 10c