Solution: Equal Sets | Sets and Functions - JEE

1. Here,  A = {2, 4, 6, 8, 10}.

The elements of set B are positive even integers less than 10. Therefore, 

B = {2, 4, 6, 8}

Since 10 ∈ A and 10 ∉ B, A and B are not equal sets.

2. Clearly, A = {A, P, L, E} and B = {L, E, A, P}

Therefore, both the sets have same elements, so A = B.

3. Elements of set A are integers whose square is less than or equal to 4. Therefore, 

A = {-2, -1, 0, 1, 2}

Elements of set B are real numbers that satisfy the equation x2 – 3x + 2 = 0. To determine the elements of set B, we need to solve the equation.

x2 – 3x + 2 = 0

=> x2 – 2x - x + 2 = 0

=> x(x - 2) - 1(x - 2) = 0

=> (x - 1)(x - 2) = 0

=> x = 1, 2

Therefore, B = {1, 2}

Clearly, A and B are not equal sets.

Trick: In case of objectives, after determining set A, we could easily have said A and B can not be equal  sets. This is because set A has 5 distinct elements and since elements of B are real values that are solution of a quadratic equation, it can have maximum of 2 distinct elements.

4.  A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}

Here 12 ∈ A and 12 ∉ B, hence A and B are not equal sets.