Multiple Choice Questions

Consider the following statements in respect of two non empty sets A and B I x notin AUB rarr x noti...........

Mathematics (NDA) Set theory

Consider the following statements in respect of two non-empty sets A and B :

I. x∉ (AUB) → x∉ or x A or x∉ B

2.x∉((A ∩ B)) → x∉ or x A and x∉ B

Which of the above statements is/are correct?

This questions was previously asked in

2022 NDA -1 Math

1 only

2 only

Both 1 and 2

Neither 1 nor 2

- Let's break down the statements to determine their correctness.

- Statement I:

- The original statement says $x \notin (A \cup B) \to x \notin A or x \notin B$ .

- Its contrapositive would be: $x \in A and x \in B \to x \in (A \cup B)$ .

- The contrapositive is false because for union, only one element needs to be in either set to be in the union.

- Therefore, Statement I is incorrect.

- Statement II:

- The original statement says $x \notin (A \cap B) \to x \notin A or x \notin B$ .

- Its contrapositive: $x \in A and x \in B \to x \in (A \cap B)$ is true.

- The original and contrapositive together make Statement II correct.

- Correct Answer: Option 2 (2 only)

Submit Error