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  4. The dual of the statement (∼ p)∧ [(∼ q)∧ (p∨ q)∧ ( ∼ r)] is

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Q. The dual of the statement $ (\sim p)\wedge [(\sim q)\wedge (p\vee q)\wedge ( \sim r)] $ is

J & K CETJ & K CET 2010Mathematical Reasoning

Solution:

In duality 'AND' is converted to 'OR' and 'OR' is converted to 'AND'.
Therefore, dual f the statement
$ (\tilde{\ }p)\wedge [(\tilde{\ }q)\,\,\wedge (p\,\vee q)\wedge (\tilde{\ }r)] $
is $ (\tilde{\ }p)\vee [(\tilde{\ }q)\,\,\vee (p\wedge q)\vee (\tilde{\ }r)] $