S∧r
S∨¬(r∧¬s)
None of These
S∧¬(r∧¬s)
Let the given expression be A = ¬s∨(¬r∧s).
The negation of A is ¬A = ¬(¬s∨(¬r∧s)).
Using De Morgan's law, ¬(P∨Q) = ¬P∧¬Q, we have:
¬A = ¬(¬s)∧¬(¬r∧s)
¬A = s∧¬(¬r∧s)
Using De Morgan's law, ¬(P∧Q) = ¬P∨¬Q, we have:
¬A = s∧(¬(¬r)∨¬s)
¬A = s∧(r∨¬s)
Using the distributive law, P∧(Q∨R) = (P∧Q)∨(P∧R), we have:
¬A = (s∧r)∨(s∧¬s)
Since s∧¬s = 0 (false), we have:
¬A = (s∧r)∨0
¬A = s∧r
Therefore, the negation of ¬s∨(¬r∧s) is equivalent to s∧r.