Verified Solution • 2025–26 Session moderate

QJEEM19Ma46e9: JEE Main 2019 Mathematics - Class 11 JEEM19Ma46e9 Solution: Let A, B and C be sets such that A B C. Then which of the…

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

Multiple Choice Options

  • A If (A – B) ⊆\subseteq C, then A ⊆\subseteq C
  • B B ∩\cap C ≠\ne ϕ\phi
  • C (C ∪\cup A) ∩\cap (C ∪\cup B) = C
  • D If (A – C) ⊆\subseteq B, then A ⊆\subseteq B

Step-by-Step Verified Solution

According to the question, we have the following Venn diagram.

Here, A∩B⊆CA \cap B \subseteq C and A∩B≠ϕA \cap B \neq \phi

JEE Main 2019 (Online) 12th April Evening Slot Mathematics - Sets and Relations Question 88 English Explanation 1
Now, from the Venn diagram, it is clear that B∩C≠ϕB \cap C \neq \phi , is true

Also, (C∪A)∩(C∪B)=C∪(A∩B)=C(C \cup A) \cap(C \cup B)=C \cup(A \cap B)=C is true.

If (A−B)⊆C(A-B) \subseteq C , for this statement the Venn diagram is

JEE Main 2019 (Online) 12th April Evening Slot Mathematics - Sets and Relations Question 88 English Explanation 2
From the Venn diagram, it is clear that if A−B⊆CA-B \subseteq C , then A⊆CA \subseteq C .

Now, if (A−C)⊆B(A-C) \subseteq B , for this statement the Venn diagram.

JEE Main 2019 (Online) 12th April Evening Slot Mathematics - Sets and Relations Question 88 English Explanation 3
From the Venn diagram, it is clear that

A∩B≠ϕ,A∩B⊆CA \cap B \neq \phi, A \cap B \subseteq C and A−C=ϕ⊆BA-C=\phi \subseteq B but A⊆BA \subseteq B

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