Let S01234 A the set of all natural numbers divisible by 2 a

Let S={0,1,2,3,4,....}, A= the set of all natural numbers divisible by 2, and B= the set of all natural numbers divisible by 3. What is the set A union B? What is the set A intersect B?

Solution

S={ 0,1,2,3,4,5,6,7...............}

A= set natural numbers divided by 2 ={2,4,6,8,........}

B=set of natural numbers divided by 3 ={3,6,9,12,..........}

A union B = {2,4,6,.....} union { 3,6,9.............} = {2,3,4,6,8,9,10,12,14,15...........}

                                                                    =S - {0,1} -(set of prime numbers -{2,3})

A intersection B = {2,4,6,8,......} intersection {3,6,9,12,.....} ={6,12,18,24,............}

                                                                                     =all natural numbers divided by 6