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

Question

The dual of the statement (∼ p)∧ [(∼ q)∧ (p∨ q)∧ ( ∼ r)] is (A)  p∧ [q∨ (p∧ q)∨ r]  (B)  (∼ p)∨ [(∼ q)∨ (p∧ q)∨ (∼ r)]  (C)  ( ∼ p)∧ [(∼ q)∨ (p∨ q)∨ r]  (D)  (∼ p)∨ [(∼ q)∨ (p∧ q)∨ r]

Tardigrade Admin · Accepted Answer

In duality 'AND' is converted to 'OR' and 'OR' is converted to 'AND'.
Therefore, dual f the statement

(~ p) \land [(~ q) \land (p \lor q) \land (~ r)]

is

(~ p) \lor [(~ q) \lor (p \land q) \lor (~ r)]

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

$p \land [q \lor (p \land q) \lor r]$

$(\sim p) \lor [(\sim q) \lor (p \land q) \lor (\sim r)]$

$(\sim p) \land [(\sim q) \lor (p \lor q) \lor r]$

$(\sim p) \lor [(\sim q) \lor (p \land q) \lor r]$

In duality 'AND' is converted to 'OR' and 'OR' is converted to 'AND'.
Therefore, dual f the statement
$(~ p) \land [(~ q) \land (p \lor q) \land (~ r)]$
is $(~ p) \lor [(~ q) \lor (p \land q) \lor (~ r)]$

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

p∧[q∨(p∧q)∨r]

(∼p)∨[(∼q)∨(p∧q)∨(∼r)]

(∼p)∧[(∼q)∨(p∨q)∨r]

(∼p)∨[(∼q)∨(p∧q)∨r]