Math CentralQuandaries & Queries


Question from Jared, a student:

If a set A={1,2,3} and set B={ {}, 1}

Can B be a subset of A? Since every Set contains an {} ?

Jared: Every set contains {} as a subset, but not necessarily as an element. Your B is the (slightly odd) set whose elements are the empty set and the natural number 1. Your A is the set whose elements are the natural numbers 1,2, and 3; it does not have the empty set as an element. Thus B is not a subset of A.

Good Hunting!


No, B is not a subset of A. As you say, every set CONTAINS
the empty set, but not every set has the empty set AS AN ELEMENT.
The empty set is an element of B, but not of A, so B is not a subset
of A.


About Math Central


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina