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Question
Let \[X = A \overline{ BC} + B\overline{ CA} + C\overline{AB } .\] Evaluate X for A = B = C = 1.
Solution
Given:
Output
\[X = A \overline{ BC} + B\overline{ CA} + C\overline{AB } .\]
A = B = C = 1
\[X = 1 . ( \overline{{1 . 1)}} + 1 . ( \overline{{1 . 1)}} + 1 . ( \overline{{1 . 1)}}\]
\[ = 1 . \bar{1} + 1 . \bar{1} + 1 . \bar{1}\]
\[ = 1 . 0 + 1 . 0 + 1 . 0\]
\[ = 0 + 0 + 0\]
\[ = 0\]
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Useful Constants and Relations:
| 1. | Charge of a proton | (e) | =1.6 × 10-19C |
| 2. | Planck's constant | (h) | = 6·6 × 10-34 Js |
| 3. | Mass of an electron | (m) | = 9·1× 10-31 kg |
| 4. | Permittivity of vacuum | (∈0) | =8 · 85 × 10-12 Fm-1 |
| 5. | `(1/(4pi∈_0))` | =9 ×109 mF-1 | |
| 6. | Permeability of vacuum | (μ0) | = 4π × 10-7 Hm-1 |
| 7. | `((mu_0)/(4pi))` | =1 × 10-7 Hm-1 | |
| 8. | Speed of light in vacuum | (c) | = 3× 108 ms-1 |
| 9. | Unified atomic mass unit | (u) |
= 931 MeV |
| 10. | Electron volt | (leV) | = 1.6 × 10-19 J |
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