# Sets Formulas For Class 11

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## Sets Formulas For Class 11

Here we are providing Sets Formula For Class 11 Maths. Practice sets problems based on these formulas. Important terms and definitions are also included so that you can revise them in a very short time.

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements.

List of Sets Formulas for Class 11

(1) A well-defined collection of objects is called a set.

(2) The objects in a set are called its elements, or members, or points.

(3) Usually, we denote sets by capital letters A, B, C, X, Y, Z, etc.

(4) A set is usually described in tabular form or set-builder form.

(5) In tabulation method, we make a list of all the objects of the set and put them within braces {}. In set-builder form, we write {x : x satisfies properties P} which means, the set of all those x such that each x satisfies properties P.

(6) A set having no element at all is called a null set, or a void set and it is denoted by Φ.

(7) A set having a single element is called a singleton set. For example, {3}.

(8) A set having finite number of elements is called a finite set, otherwise it is called an infinite set. The number of elements in a finite set A is denoted by n(A).

(9) Two sets A and B having exactly the same elements are known as equal sets and we write, A=B.

(10) A set A is called a subset of a set B, if every element of A is in B and we write, A⊆B .

(11) If A is a subset of set B and A≠B ! then A is called a proper subset of set B and we write, A⊂B.

(12) The total number of subsets of a set A containing n elements is 2n.

(13) The collection of all subsets of a set A is called the power set of A, to be denoted by P(A).

(14) Let a and b be real numbers such that a<b, then

(15) The union of two sets A and B, denoted by A∪B, is the set of all those elements which are either in A or in B or in both A and B.
A∪B = {x : x ∈ A and x ∈ B}.

(16) The intersection of two sets A and B, denoted by A∩B, is the set of all those
elements which are common to both A and B.
A∩B= {x : x∈ A and x ∈ B}

(17) The difference between two sets A and B, denoted by (A-B), is defined as
(A-B )={x : x ∈ A and x ∈ B}
Similarly, (B-A)={x : x ∈ B and x ∉ A}

(18) The symmetric difference between the sets A and B, denoted by A Δ T , is
defined as A Δ B = (A-B)∪(B-A). ,

(19) Let A be a subset of the universal set U. Then the complement of A, denoted
by A’, or Ac, or U – A, is defined as A’ = {x : x ∈ U and x ∉ A}.

(20) Various laws of operations on sets

(21) For any two sets A and B, we have

(22) For any three sets A, B and C, we have

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – {n(A∩B)+n(B∩C)+n(A∩C)} + n(A∩B∩C)

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