Example:
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Algebra of statements
The following are some important logically equivalent propositions.1.
2.
3.
4.
5.
6.
7.
Proof of De Morgan's laws
Observe that last two columns are identical.
Observe that last two columns are identical.
Duality
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.
Illustration 1:
are dual of each other w.r.t. connectives '
' and '
'.
Illustration 2:
The logical equivalences
each other w.r.t. connectives '
' and '
'.Example 1:
By using laws of algebra of statements, show that
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Example 2:
By using laws of algebra of statements, show that
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