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Let S*(p, q, r) be the dual of the compound statement S(p, q, r), where S(p, q, r) = (~p) AND (~(q OR r)). Then S*(~p, ~q, ~r) is logically equivalent to:

1. S(p, q, r)
2. ~S(~p, ~q, ~r)
3. ~S(p, q, r)
4. S*(p, q, r)

Correct answer: ~S(p, q, r)

Solution

Taking the dual and substituting negated variables and simplifying with De Morgan's laws gives the negation of the original statement, ~S(p, q, r).

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