Verified Solution • 2025–26 Session moderate

QJEEM20Ma25ea: JEE Main 2020 Mathematics - Class 11 JEEM20Ma25ea Solution: Let A, B, C and D be four non-empty sets. The contrapositive…

Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A ⊆\subseteq B and B ⊆\subseteq D, then A ⊆\subseteq C" is :

Multiple Choice Options

  • A If A ⊈ C, then A ⊈ B or B ⊈ D
  • B If A ⊈ C, then A ⊈ B and B ⊆\subseteq D
  • C If A ⊆\subseteq C, then B ⊂\subset A or D ⊂\subset B
  • D If A ⊈ C, then A ⊆\subseteq B and B ⊆\subseteq D

Step-by-Step Verified Solution

Contrapositive of p →\to q is ~q →\to ~p

If A ⊆\subseteq B and B ⊆\subseteq D, then A ⊆\subseteq C means

(A ⊆\subseteq B) ∧\wedge (B ⊆\subseteq D) →\to (A ⊆\subseteq C)

Contrapositive is

∼\sim (A ⊆\subseteq C) →\to ∼\sim (A ⊆\subseteq B) ∨\vee ∼\sim (B ⊆\subseteq D)

⇒\Rightarrow A ⊈ C →\to (A ⊈ B) ∨\vee (B ⊈ D)

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