Question

If A = {x : x is square of natural numbers ≤ 8}, and B = {2x + 1 : x ∈ N}, the what is (A ∩ B)?
1. {0, 1, 4, 9, 25, 49, 121}
2. {1, 4, 16, 36, 64}
3. {9, 25,49}
4. {1, 9, 25, 49}

Answer 1

Correct Answer - Option 3 : {9, 25,49}

Concept:

Set theory:

• A ∪ B means set of all the values in the set A and B.
• A ∩ B is the set of common elements of A and B.
• Subset (⊂) is the set such that all the elements of the subset are in the set from which the subset is taken from.

 

Calculation

Given: B = {2x + 1 : x ∈ N}

So, Set B = {3, 5, 7, 9, 11, 13, ......} (all the odd positive integers excluding 1)

Given: A = {x : x is square of natural numbers ≤ 8}

So, Set A = {1, 4, 9, 16, 25, 36, 49, 64}

∴ A ∩ B = {9, 25, 49}