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The notation NAND stands for "Not And." The NAND connective, denoted ↑, is defined by the following truth table: 1. P P↑ Q F F F T F F Use a truth table to show that P ↑ Q is logically equivalent to ¬(P A Q). а.

The notation NAND stands for "Not And." The NAND connective, denoted ↑, is defined by the following truth table: 1. P P↑ Q F F F T F F Use a truth table to show that P ↑ Q is logically equivalent to ¬(P A Q). а.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Understanding NAND: "Not And" Logic Connective 1. **The notation NAND** stands for "Not And." The NAND connective, denoted by the symbol ↑, is defined by the following truth table: | **P** | **Q** | **P ↑ Q** | |-------|-------|----------| | F | F | T | | F | T | T | | T | F | T | | T | T | F | - **Explanation of the Truth Table**: - When both P and Q are false (F), P ↑ Q is true (T). - When P is false (F) and Q is true (T), P ↑ Q is true (T). - When P is true (T) and Q is false (F), P ↑ Q is true (T). - When both P and Q are true (T), P ↑ Q is false (F). - This demonstrates how the NAND operation results in true except when both operands are true. a. **Exercise**: - Use a truth table to show that \( P ↑ Q \) is logically equivalent to \( \neg (P ∧ Q) \), meaning the NAND operation can be understood as the negation of the AND operation.
Transcribed Image Text:### Understanding NAND: "Not And" Logic Connective 1. **The notation NAND** stands for "Not And." The NAND connective, denoted by the symbol ↑, is defined by the following truth table: | **P** | **Q** | **P ↑ Q** | |-------|-------|----------| | F | F | T | | F | T | T | | T | F | T | | T | T | F | - **Explanation of the Truth Table**: - When both P and Q are false (F), P ↑ Q is true (T). - When P is false (F) and Q is true (T), P ↑ Q is true (T). - When P is true (T) and Q is false (F), P ↑ Q is true (T). - When both P and Q are true (T), P ↑ Q is false (F). - This demonstrates how the NAND operation results in true except when both operands are true. a. **Exercise**: - Use a truth table to show that \( P ↑ Q \) is logically equivalent to \( \neg (P ∧ Q) \), meaning the NAND operation can be understood as the negation of the AND operation.
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