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Question
Prove that the following statement pattern is equivalent :
(p ∨ q) → r and (p → r) ∧ (q → r)
Solution
Truth table given is as follows:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| p | q | r |
`A=p vv q` |
`B=p->r` |
`C=q->r` |
`A->r` |
`B ^^ C` |
| T | T | T | T | T | T | T | T |
| T | T | F | T | F | F | F | F |
| T | F | T | T | T | T | T | T |
| T | F | F | T | F | T | F | F |
| F | T | T | T | T | T | T | T |
| F | T | F | T | T | F | F | F |
| F | F | T | F | T | T | T | T |
| F | F | F | F | T | T | T | T |
In the above truth table all the entries in the columns of
(p ∨ q) → r and (p → r) ∧ (q → r) are identical.
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
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