Question

# If A = {x : x N, x is a factor of 6} and B = {x N : x is a factor of 8} then is

- {1, 2}
- {1}
- {2}
- {0}

Hint:

### We are give set builder form of two sets. We have to find the intersection of the two sets. We will first write the rooster form or in other words, the elements of the sets in a bracket. Then we will find the intersection.

## The correct answer is: {1}

### The given set is

A={x : x ∈ N, x is a factor of 6)

B (x ∈ N : x is a factor of 8)

We have to find the intersection of the two sets.

We will write the roster form or elements of the both the sets first.

Set A

x is a factor of 6 and it belongs to N means a natural number.

Factor means the numbers which divide the given number and leave remainder zero.

The factors of 6 are 1, 2, 3, and 6.

So, the roster form of it will be

A = { 1, 2, 3, 6}

Set B

x is a factor of 8. It belongs to natural numbers.

The factors of 8 are 1, 2, 4, 8

So, the roster form of it will be

B = { 1, 2, 4, 8}

Now, we have to find A∩B

It means we have to find the elements that are common to both the sets

The elements that are common to both the sets are 1 and 2

A ∩ B = {1, 2}

This is the required answer.

When we have to find intersection of two sets, we have to find their common elements. When we have to find union of two sets, we have to consider all the elements of both the sets.

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