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JEE Main 20207 JanuaryEvening Shift

Exam: JEE Main
Year: 2020
Date: 7 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2020 · 7 January · Evening Shift · Mathematics · Mathematical Reasoning

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 ⊆ B

and

B ⊆ D

, then

A ⊆ C

” is

Options

AIf $A ⊈ C$ , then $A ⊆ B$ and $B ⊆ D$
BIf $A ⊆ C$ , then $B ⊂ A$ and $D ⊂ B$
CIf $A ⊈ C$ , then $A ⊈ B$ and $B ⊆ D$
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 \left(P ∧ Q\right) \to R $is$

$~ R \to ~ \left(P ∧ Q\right) = ~ R \to$ \left(~ \left(P\right) $∨ ~ \left(Q\right)\right)$

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