Question

Set A contains multiples of 10 from 10 to 90. Set B contains multiples of 30 from 30 to 120. Set C contains even numbers from 2 to 20. Find (A ∪ B) ∩ C.

Answer 1

Step-by-step explanation

Set A contains multiples of 10 from 10 to 90:

`A=\lbrace10,20,30,40,50,60,70,80,90\rbrace`

Set B contains multiples of 30 from 30 to 120:

`B=\lbrace30,60,90,120\rbrace`

The union of two sets is the set that contains all the values in both sets. Therefore, A U B is:

`A\cup B=\lbrace10,20,30,40,50,60,70,80,90,120\rbrace`

Set C contains even numbers from 2 to 20:

`C=\lbrace2,4,6,8,10,12,14,16,18,20\rbrace`

The intersection of two sets is the set of values that exist in the two sets. Therefore, (A U B) n C is:

`(A\cup B)\cap C=\lbrace10,20\rbrace`

That is the answer.