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99 Percentile Qs Bank for JEE MainMathematicsSets and Relations

Let A ,   B and C   be sets such that ϕ ≠ A ∩ B ⊆ C . Then which of the following statements is not true?

Options

  1. AB ∩ C ≠ ϕ
  2. B( C ∪ A ) ∩ ( C ∪ B ) = C
  3. CIf ( A - B ) ⊆ C , then A ⊆ C
  4. DIf ( A - C ) ⊆ B , then A ⊆ B

Correct answer

D. If ( A - C ) ⊆ B , then A ⊆ B

Step-by-step solution

For A = C , A - C = ϕ ⇒ ϕ ⊆ B But A ⊈ B Hence, If ( A - C ) ⊆ B , then A ⊆ B is not true Let x ∈   C ,     ⇒ x ∈ C ∪ A ∩ C ∪ B ⇒ x ∈ C ∪ A   and x ∈ C ∪ B ⇒ ( x ∈ C   or x ∈ A ) and ( x ∈ C or   x ∈ B ) ⇒   x ∈ C or   x ∈ A ∩ B ⇒ x ∈ C or x ∈ C    a s   A ∪ B ⊆ C &#

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