Question

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

• A. $p\wedge [q\vee (p\wedge q)\vee r]$
• B. $(\sim p)\vee [(\sim q)\vee (p\wedge q)\vee (\sim r)]$
• C. $( \sim p)\wedge [(\sim q)\vee (p\vee q)\vee r]$
• D. $(\sim p)\vee [(\sim q)\vee (p\wedge q)\vee r]$

Answer 1

Answer: (B)

$(\sim p)\vee [(\sim q)\vee (p\wedge q)\vee (\sim r)]$

Answer 2

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 $(\tilde{\ }p)\vee [(\tilde{\ }q)\,\,\vee (p\wedge q)\vee (\tilde{\ }r)]$