Question

If A = {x : x ∈ N and x is a prime number < 5} and B = {y : y ∈ R and y² - 5y + 6 = 0} then which of the following is true ?
1. A = B
2. A ⊂ B
3. B ⊂ A
4. None of these

Answer 1

Correct Answer - Option 1 : A = B

Concept:

Equal Sets: Any two sets are said to be equal sets if and only if they are equivalent and as well as their elements are same.

Calculation:

Given: A = {x : x ∈ N and x is a prime number < 5} and B = {y : y ∈ R and y2 - 5y + 6 = 0}

So, the given set A can be re-written as: A = {2, 3}

As we know that, B = {y : y ∈ R and y2 - 5y + 6 = 0}

⇒ y2 - 3y - 2y + 6 = 0

⇒ y(y - 3) - 2(y - 3) = 0

⇒ (y - 2) (y - 3) = 0

⇒ y = 2 or 3

⇒ B = {2, 3}

As we know that, any two sets are said to be equal sets if and only if they are equivalent and as well as their elements are same.

So, A = B

Hence, option 1 is the correct answer.