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b. T (P T Q) = P A Ų c. (P ↑ P) ↑ (Q ↑ Q) = P v Q d. P↑ (Q ↑ Q) = P → Q

b. T (P T Q) = P A Ų c. (P ↑ P) ↑ (Q ↑ Q) = P v Q d. P↑ (Q ↑ Q) = P → Q

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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The NAND connective is important because it only takes two transistors to build an electronic circuit that computes the NAND of two signals: ww- Vcc pTq Such a circuit is called a logic gate. Moreover, it is possible to build logic gates for the other logical connectives entirely out of NAND gates. Demonstrate this by proving the 1 following equivalences in parts (b), (c), and (d) using the laws of the logical equivalence and the fact that P ↑ Q = ¬(PA Q). b. (P ↑ Q) ↑ (P ↑ Q) = P A Q c. (P ↑ P) ↑ (Q ↑ Q) = P v Q d. P↑ (Q ↑ Q) = P → Q
Transcribed Image Text:The NAND connective is important because it only takes two transistors to build an electronic circuit that computes the NAND of two signals: ww- Vcc pTq Such a circuit is called a logic gate. Moreover, it is possible to build logic gates for the other logical connectives entirely out of NAND gates. Demonstrate this by proving the 1 following equivalences in parts (b), (c), and (d) using the laws of the logical equivalence and the fact that P ↑ Q = ¬(PA Q). b. (P ↑ Q) ↑ (P ↑ Q) = P A Q c. (P ↑ P) ↑ (Q ↑ Q) = P v Q d. P↑ (Q ↑ Q) = P → Q
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