Question

Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}. What is A ∩ B?

Answer 1

`A=\{1,3,5,\ldots,99\}\\B=\{50,55,\ldots,150\}\\\\A\cap B=\{55,65,75,85,95\}`

Answer 2

`A\bigcap B=\left \{ 55,65,75,85,95 \right \}`

Explanation:

Set A contains odd numbers between 0 and 100.

So, the elements in set A are as, Set A
`=\left \{ 1,3,5,7,9,11,13,15,...99 \right \}`

Set B contains the numbers between 50 and 150, that are evenly divisible by 5.

So, the elements in set B are are as, Set B

`=\left \{ 55,60,65,70,75,80,85,90,... 145\right \}`

Now, we need to find
`A\bigcap B`

To find
`A\bigcap B` , we need to find the common elements in Set A and Set B.

The common elements in Set A and Set B is
`\left \{  55,65,75,85,95 \right \}`

So,
`A\bigcap B=\left \{ 55,65,75,85,95 \right \}`