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प्रश्न
Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
उत्तर
Let p : D is dog.
q : D is very good.
Then the given statement in the symbolic form is
- p → q
- q → p
- ~q → ~p
- ~p → ~q
| p | q | ~p | ~q | p → q | q → p | ~q → ~p | ~p → ~q |
| T | T | F | F | T | T | T | T |
| T | F | F | T | F | T | F | T |
| F | T | T | F | T | F | T | F |
| F | F | T | T | T | T | T | T |
Since the entries in (i) and (iii) columns are the same, they have the same meaning.
Also, the entries in (ii) and (iv) columns are the same. they have the same meaning.
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