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COMEDK202510 May 2025Morning ShiftMathematicsSets and RelationsActual

Identify the correct statement

Options

  1. AA A^ =
  2. B(A B)^ =A^ B^
  3. CA B B^ A^
  4. DA-B=A^ B

Correct answer

C. A B B^ A^

Step-by-step solution

Analyze each option based on set theory principles. Option (1): A A^ = U , where U is the universal set. Thus, A A^ = is false. Option (2): According to De Morgan's Law, (A B)^ = A^ B^ . Thus, (A B)^ = A^ B^ is false. Option (3): If A B , then every element of A is an element of B . Consequently, any element not in B must also not be in A . This implies B^ A^ . This statement is true. Option (4): The set difference A - B is defined as A B^ . The statement A - B = A^ B is false. Answer: A B B^ A^

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