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JEE Main20207 Jan 2020Evening ShiftMathematicsMathematical ReasoningActual

Let A , B , C and D be four non-empty sets. The contrapositive statement of “If A ⊆ B and B ⊆ D , then A ⊆ C ” is

Options

  1. AIf A ⊈ C , then A ⊆ B and B ⊆ D
  2. BIf A ⊆ C , then B ⊂ A and D ⊂ B
  3. CIf A ⊈ C , then A ⊈ B and B ⊆ D
  4. DIf A ⊈ C , then A ⊈ B or B ⊈ D

Correct answer

D. If A ⊈ C , then A ⊈ B or B ⊈ D

Step-by-step solution

Let P = A ⊆ B , Q = B ⊆ D , R = A ⊆ C Contrapositive of P ∧ Q → R is ~ R → ~ P ∧ Q = ~ R → ~ P ∨ ~ Q

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