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| Logical Equivalence and Duality |
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| Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are
logically equivalent, then it is represented by p º
q. |
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| Example: |
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| Observe that last two columns are identical. |
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| The following are some important logically equivalent propositions. |
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| 6. |
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| 7. |
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| Observe that last two columns are identical. |
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| Observe that last two columns are identical. |
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| Two logical equivalences are said to be dual of each other with respect to two connectives if one equivalence can be obtained by the other equivalence, just by interchanging the connectives. |
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| Illustration 1: |
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 are dual of each other w.r.t. connectives ' ' and ' '. |
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| Illustration 2: |
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| The logical equivalences |
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 each other w.r.t. connectives ' ' and ' '. |
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| Example 1: |
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| By using laws of algebra of statements, show that |
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| Example 2: |
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| By using laws of algebra of statements, show that |
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