Question

Let S = {0,1,2,3,4,...}, A = the set of natural numbers divisible by 2, and B = the set of numbers divisible by 5. What is the set A intersection B? What is the set A union B? Please show your work.

Answer 1

Let S = {0,1,2,3,4,...},

A = the set of natural numbers divisible by 2

i.e A={ 0,2,4,6,8,10......} all even numbers

, and B = the set of numbers divisible by 5.

i.e B={0,5,10,15,20..........}

All the numbers ending with 0 and 5

What is the set A intersection B?

Since the numbers ending with 5 are not divisible by 2. only the numbers ending with 0 are divisible by both 2 and 5.

So A n B = {0,10,20,30.............} i.e all numbers ending with 0

What is the set A union B?

A U B includes all the numbers in A and all numbers in B . Since the numbers in B ending with 0 are divisible by 2 , no need to repeat those numbers in A U B

So, it includes all even numbers and all numbers ending with 5

So, A U B ={ 0,2,4,5,6,8,10,12,14,15,16, 18,20 ....}