In the early twentieth century, John-Euler Venn solved the word problems in arithmetic with the help of Venn-diagram. This method grew popular as it is easy to understand and simple to calculate. So, Venn-diagram is associated with his name.
A set which does not contain any element is called an empty set or null set. It is denoted by \(\emptyset\)
empty, and is read as phi. In roster form, \(\emptyset\) it is denoted by { }.
For example:
Note \(\emptyset\) ≠ { 0 } { 0 } is a set having one element. |
A set which has only one element is called singleton set.
For example:
A set which contains a definite number of elements is called a finite set. The empty set is also called a finite set.
For example:
A set which contains never ending element is called infinite set.
For example:
The number of distinct element in a given set A is called the cardinal number of A. It is denoted by n(A).
For example:
Two set are called to be equivalent if their cardinal number is same i.e. n(A)=n(B). The symbol for denoting an equivalent set is '\(\leftrightarrow\)'.
For example:
A = {1, 2, 3, 4, 5}
B={a, b, c, d, e }
Therefore, A \(\leftrightarrow\) B.
Two set are said to be equal if they contain the same element. Every element of a set A has every element of B and every element of B has every element of A.
For example:
A= { a,e, i,o, u }
B= {u, i, o, a, e}
\(\therefore\) A = B
.
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