Introduction to Sets and Subsets

WELCOME Grade 9-11 students

In today’s blog, we are going to look at Sets and Subsets.  

Sets

Sets can be seen as a collection of elements or objects, that have some characteristics in common and it is normally denoted by a capital letter.  A set may be defined by listing the members or describing them and a set can be well-defined when all its members can be listed. 

A flock of sheep is an example of a defined set while even numbers less than 13 is an example of well-defined set. 

 

Introducing Subset

A subset can be defined as a part of a given set, another set or the same set.  It is normally represented by the symbol ⊆. If all elements of set X are in another set Y, then set X is said to be a subset of set Y.  

For Example,

X consist of {a, e, r} and Y consist of {a, d, e, r} therefore, X is a

subset of Y because all the elements of X are present in the set Y.  

The Number of Subsets

If P= {a, b, c}, then the subsets of P are:

- {a}

-{b}

-{c}

-{a,b}

-{a,c}

-{b,c}

-{}

-{a,b,c}

This indicates that every set is a subset of itself and that the empty set ({}) is a subset of all sets.  The first six subsets of P are called proper subsets and the last two subsets of P are called improper subsets.  Proper subsets can be defined as one that contains a few elements of the original set while improper subsets is one that contains every element in the original set.

 

Practice Questions

1.  If A= {2,4,6,8} and B= {2,4,6,8,10,12}. State whether the statement A ⊆ B is true or false?

2.  Given that the set T= {5, 7, 8, 10, 15} calculate the number of possible subsets of T.