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| Summary |
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- A well-defined collection of definite objects is called a set.
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- In roster method of representing a set, all the elements are listed in the set.
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- In property method of representing a set, all the elements are represented by stating all the properties which are satisfied by the elements of the set and not by any other element.
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- finite set if it contains only finite number of elements. |
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- infinite set if it contains infinitely many elements. |
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- null set if it does not contain any element. |
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- singleton set if it contains only one element. |
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- Equivalent sets if the elements of one set can be put in one-one correspondence with the elements of the other set. |
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- Equal sets if every element of one set is in the other set and
vice-versa |
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- A set A is said to be a subset of set B
if every element of A is an element of B. If A is subset of B, then it is
expressed as A Í B.
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- A set A is said to be a proper subset of set B if A is a subset of B
and A is not equal to B. If A is a proper subset of B, then we write A
Ì B.
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In order to show that A Ì B it is sufficient to
show that each element of A is in B and there is at least one
element in
B, which is not in A. |
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- The union of two sets A and B is defined as the set of all those elements which are in either A or B or both. |
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- The intersection of two sets A and B is defined as the set of all those elements which are in both A and B. |
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- The difference of two sets A and B, in this order, is the set of all those elements of A which are not in B. |
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- The symmetric difference of two sets A and B is defined as the union of the sets A - B and B - A. |
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- If A is a subset of universal set X, then complement of A is defined
as the set of all those elements of X which are not in A and it denoted
by A' or by Ac. We have A' = X - A.
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| Symbolically, |
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- Let A, B be finite sets. Then
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- Let A,B,C be finite sets.
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