Set Theory And Logic

Step 1: The given expression is .

Step 2: To find the negation, apply De Morgan's law. The negation of a disjunction ( ) becomes a conjunction ( ) of the negations of each term. So we need to negate each term separately:

Step 3: Simplify to . Now apply De Morgan's law to , which becomes , i.e., . Therefore, the expression becomes:

Step 4: However, the original expression has outside the parentheses, so this simplifies to:
Thus, the negation is , which is option (c).