Question

If C = {integers divisible by 6 from 1 to 30} and D = {integers divisible by 3 from 1 to 20}, what is C n D?

Answer 1

Well, you're told that C = {integers divisible by 6 from 1 to 30}. Could we list those integers?

Answer 2

integers divisible by 6 from 1 to 30 is 6,12,18,24,30

Answer 3

That's correct! So another way of expressing C would be C = {6, 12, 18, 24, 30}. Now, since D = {integers divisible by 3 from 1 to 20}, could we also list the integers of that set?

Answer 4

integers divisible by 3 from 1 to 20 is 3,6,9,12,15,18

Answer 5

Excellent! Now we know that C = {6, 12, 18, 24, 30} and D = {3, 6, 9, 12, 15, 18}. In simple terms, the definition of intersection, \(A\cap B\), is the terms that both A and B have in common. What terms do the sets C and D have in common?\[\]

Answer 6

6,12,18

Answer 7

You got it. :)

Now to formalize that a bit, we'd write it like this: \(A\cap B=\{6,12,18\}\).\[\]

Answer 8

Oh my gosh, thank you(:

Answer 9

You're most welcome!