Properties of Sets
A set which contains all the sets under consideration is called the Universal set.
A rectangle is used to represent the universal set.
If every element of set A is in set B, then A is said to be the subset of B.
The symbol ⊆ is used to denote subset.
If A is a subset of B then we can say that B is the superset of A as it contains all the elements of A.
The symbol ⊇ is used to denote superset.
Set A is said to be the proper subset of set B, if all the elements of set A are in set B and set B contains at least one extra element more, which is not in set A.
The symbol ⊂ is used to denote proper subset.
Number of Subsets
of a set
If a set has n elements then the number of subsets of the set will be 2n.
And the number of proper subsets will be 2n - 1
Every set is a subset of itself and an empty set is a subset of every set.
The set containing all the possible subsets of a given set is called a power set.
The power set of a set S is denoted by P(S).
Complement of a set
The complement of set A is the set of all the elements which do not belong to A but belong to the universal set U.
It is represented by A' (read as A complement).
For any two sets A and B.
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A) + n(A') = n(U)
n(A∪B)' = n(U) - n(A∪B)
n(A∩B)' = n(U) - n(A∩B)
De Morgan's First Law.
(A∪B)' = A'∩B'
The complement of the union of two sets A and B is equal to the intersection of the complements.
De Morgan's Second Law.
(A∩B)' = A'∪B'
The complement of the intersection of the two sets A and B is equal to the union of the complements.
More from Grade 7 Math
Sets are around us, everywhere. Learn how they are formed, named, and represented.
All you need to know about lines, parallel, perpendicular and intersecting lines. Along with all the examples from the world around you.
Learn about the different types of angles acute, right, obtuse and more through exciting facts from the Wonders of the World.