Question

A = {Prime numbers between 10 and 16} B = {Multiples of 3 between 10 and 16}

(a) List the members of AUB.
(b) What is AB?
(c) Is it true that 11 € B?​

Answer 1

Part (a)

A = {prime numbers between 10 and 16}

A = {11, 13}

B = {multiples of 3 between 10 and 16}

B = {12, 15}

A U B = union of set A with set B

A U B = {set of stuff from A or B or both}

A U B = {11, 12, 13, 15}

=================================================

Part (b)

I'm assuming that you meant to write
`A \cap B`

If so, then this is the set of values inside set A and set B at the same time.

Since there is no common overlap between the sets A and B, we say that the answer is the empty set. We write the empty set as a pair of curly braces with nothing inside. Not even zero is a member of the empty set.

`A \cap B = \{ \ \}`

we could also write the empty set using the symbol
`\varnothing`

So,

`A \cap B = \varnothing`

=================================================

Part (c)

Answer: False

Reason:

The weird looking E symbol in this context means "is inside" or "is part of"

In other words, a statement like
`11 \in B` translates to "11 is part of set B", which is a false statement. Recall that B = {12, 15}

If we said
`11 \in A`, then it would be true since A = {11, 13} which shows 11 as one of the values of set A.