The Null or Empty Set

There are some sets that do not conatin any element at all. For example, the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } or Ø .

Some other example of null sets are:

The set of dogs with six legs.

The set of squares with 5 sides.

The set of cars with 20 doors.

The set of integers which are both even and odd.

Set Equality

Consider the sets:

P ={Tom, Dick, Harry, John} Q = {Dick, Harry, John, Tom}

Since P and Q contain exactly the same number of members and the memebers are the same, we say that P is equal to Q, and we write P = Q. The order in which the members appear in the set is not important.

Consider the sets:

R = {2, 4, 6, 8} S = {2, 4, 6, 8, 10}

Since R and S do not contain exactly the same members, we say that R is not equal to S and we write R ≠ S.

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