Venn diagrams can be very helpful in solving problems, and they are the best way of showing which members belong to different sets. Lets look at an example with our teacher. The rectangle around the outside represents the universal set, which is denoted by the symbol ξ.

Any shapes within shapes are subsets.

First we will look at universal sets that contain only a single subset.

Exercise 1

Subsets

As well as the symbol ∈ we have the symbol ⊂ which has a different meaning.

x ∈ X means that x is a member of X

y ⊂ X means that y is a subset of X

So {2,3} ⊂ {1,2,3} is true, but {2,3} ∈ {1,2,3} is not true

Exercise 2

Answers