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3. (a) Prove with Boolean algebra the consensus theorem x• y + x'•z+ y z=x•y+x' · z. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 6. (a) Prove with Boolean algebra that (x + y) (x' + y) = y. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 8. *(a) Draw a three-input OR gate, its Boolean expression, and its truth table, as in Figure 10. (b) Do part (a) for the three-input NAND gate. (c) Do part (a) for the three-input NOR gate.

3. (a) Prove with Boolean algebra the consensus theorem x• y + x'•z+ y z=x•y+x' · z. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 6. (a) Prove with Boolean algebra that (x + y) (x' + y) = y. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 8. *(a) Draw a three-input OR gate, its Boolean expression, and its truth table, as in Figure 10. (b) Do part (a) for the three-input NAND gate. (c) Do part (a) for the three-input NOR gate.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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3 (a and b), 6 (a and b), 8 (a, b and c)

3. (a) Prove with Boolean algebra the consensus theorem x• y + x'•z+ y z=x•y+x' · z. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 6. (a) Prove with Boolean algebra that (x + y) (x' + y) = y. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 8. *(a) Draw a three-input OR gate, its Boolean expression, and its truth table, as in Figure 10. (b) Do part (a) for the three-input NAND gate. (c) Do part (a) for the three-input NOR gate.
Transcribed Image Text:3. (a) Prove with Boolean algebra the consensus theorem x• y + x'•z+ y z=x•y+x' · z. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 6. (a) Prove with Boolean algebra that (x + y) (x' + y) = y. Give a reason for each step in your proof. (b) Show the dual proof of part (a). 8. *(a) Draw a three-input OR gate, its Boolean expression, and its truth table, as in Figure 10. (b) Do part (a) for the three-input NAND gate. (c) Do part (a) for the three-input NOR gate.
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