Sets - basic

So, we have the set A. The things in set A are called ELEMENTS of set A.

Let's say:

A = {months of the year with less than 31 days}

List the elements of A.

So, we list the months of the year with less than 31 days, like this:

A = {February, April, June, September, November}

And that's it! However some set questions are harder (even the basic ones):

List the elements of A = {𝑥 : 𝑥 + 2 < 10}

This looks very confusing. Basically it means:

A is the set of numbers 𝑥, and 𝑥 + 2 is less than 10.

But to do this, we need to know the universal set, which is all the possible elements of A. The symbol for this is 𝜉. So, say 𝜉 = {𝑥 : 𝑥 is a prime number and is positive}.

This means that, out of all positive prime numbers, only the ones that add up to less than 10 when you add 2 belong to set A.

So, 𝑥 must be 7 or less. (8 + 2 = 10, so all elements of A must be less than 8).

The first five prime numbers are 2, 3, 5, 7 and 11. 11 isn't in A, because 11 + 2 = 13, but 2, 3, 5 and 7 are.

This means that A = {2, 3, 5, 7}.

We will do sets with Venn diagrams next time! Use our quiz to test yourself: