NDA 2019 Paper 1 | Sets, Relations and Functions Question 34 | Mathematics

Let X be a non-empty set and let A, B, C be subsets of X. Consider the following statements.

1. $$A \subset C \Rightarrow (A \cap B) \subset (C \cap B),\,(A \cup B) \subset (C \cup B)$$

2. $$(A \cap B) \subset (C \cap B)$$ for all sets $$B \Rightarrow A \subset C$$

3. $$(A \cup B) \subset (C \cup B)$$ for all sets $$B \Rightarrow A \subset C$$

Which of the above statements are correct?

Only 1 and 2

Only 2 and 3

Only 1 and 3

1, 2 and 3

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If A = {$$\lambda$$, {$$\lambda$$, $$\mu$$}}, then the power set of A is

{$$\phi$$, {$$\phi$$}, {$$\lambda$$}, {$$\lambda$$, $$\mu$$}}

{$$\phi$$, {$$\lambda$$}, {$$\lambda$$, $$\mu$$}, {$$\lambda$$, {$$\lambda$$, $$\mu$$}}}

{{$$\lambda$$}, {$$\lambda$$, $$\mu$$}, {$$\lambda$$, {$$\lambda$$, $$\mu$$}}}

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

In a school, all the students play atleast one of thee indoor games - chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.

What can be the minimum number of students in the school?

123

111

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What can be the maximum number of students in the school?

111

123

125

135

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