Test: Operations On Sets - JEE MCQ

{1,3,5}&{2,4,6} are disjoint sets.

Explanation:

In {1,3,5} & {1,3,6} 1 and 3 is the same numbers.

In {1,2,3} & {1,2,3} 1,2 and 3 is the same numbers.

In {1,3,5} & {2,3,4} 3 is the same number.

In {1,3,5} & {2,4,6} not any numbers are same.

First which region is over which region Then We will see that A is on the B so A intersection B and after C is on the A so, A intersection C after that we have to take all intersection part so A intersection B is Union with A intersection C.

The shaded region represents (A ∩ B) ∪ (A ∩ C).

P U Q means P Union Q In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.

Since, y = e^x and y = x do not meet for any x ∈ R ∴ A ∩ B = φ.

The intersection of the sets A and B, is the set containing those elements that are in both A and B.

Correct Answer :- B

Explanation:- B = {3,5,6,7}   C = {7,8,9}

A = {2,4,6,8}

A⋂(B⋂C) = {6,8}

A ∩ B = {4, 3}

Probability of event A or B

The probability that Events A and B both occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B). If Events A and B are mutually exclusive, P(A ∩ B) = 0. The probability that Events A or B occur is the probability of the union of A and B.

The expression A ∩ B' denotes the elements that are in A but not in B. When you take the intersection of A with A ∩ B', you're essentially filtering A by itself (which does nothing to A) and then further by the condition that elements are not in B.

So, the result will still be the elements that are in A but not in B, since all elements of A ∩ B' are by definition in A. Therefore, A ∩ (A ∩ B') is equivalent to A ∩ B', which is Option A in your list of options.