1. A set "A" is a subset of B, if and only if every element of A is also an element of B, and is denoted by A Ì B.
Example:
A = {a,e,i,o,u}, B = {a,b,c,d,e,f,g,h,...........,z}
All the elements in the set A are in set B.
a Î A and a Î B
e Î A and e Î B
i Î A and i Î B
o Î A and o Î B
u Î A and u Î B
\ A Ì B [Read as A subset of B]
The above statement is also expressed as B contains A this is written as B É A and read as B is super set of A.
2. Every set is a subset of itself.
Example:
A = {1,2,3}, B = {1,2,3}
Every element of A is also an element of B.
\ A Ì B (I)
Similarly every element of B is also in A.
\ B Ì A (II)
From the above tow statements A = B
\ Every set is a subset of itself.
3. Y Ì X and Y¹ X, then Y is called the proper subset of X.
Example:
X = {1,2,3,4}, Y = {3,4}
From above two sets every element of Y is also an element of X.
\ Y Ì X
And we observe that the two sets are not equal i.e.Y¹ X.
4. A is not a subset of B if A contains at least one element which is not in B.
A Ë B or B Ë A.
5. The empty set is a subset of every set.
Directions: Check the given statements true or false. Also write at least ten examples of your own.
