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2 votes
2 votes
20) If S d is a dual of S then (S d )d ⇔
a) ~S b) S c) T d) F

2 Answers

1 votes
1 votes

My understanding is it should be S

e.g.:

S = ~((~a+b.c)+d)
Sd = ~((~a.(b+c)).d)

if we take dual again it should fetch S.

Therefore answer is B

1 votes
1 votes
Let's suppose  $\text{S = A + B}$

Dual of $\text{S}$ is $\text{S}_d = \text{A} \cdot \text{B}$

Dual of $\text{S}_d$ is $(\text{S}_d)_d = \text{A + B = S}$

 If $\text{S}_d$ is a dual of $\text{S}$ then $(\text{S}_d)_d  \Leftrightarrow \text{S}$

$\textbf{NOTE:}$ The dual of the compound proposition that contains only the logical operators $∧, ∨, \sim$ is the proposition obtained by replacing each $∨, ∧,$ by each $∧, ∨.$ Each $\text{T}$ by $\text{F}$ and each $\text{F}$ by $\text{T}.$ But negation remains unchanged.
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