Set language.pdf
- 2. TABLE OF CONTENTS Set 1.1 Definition 1.1.1 Examples of Set 1.1.2 Mathematical Sets 1.2 Types of Sets 1.2.1 Empty Set or Null Set 1.2.2 Singleton Set 1.2.3 Finite Set 1.2.4 Infinite Set 1.2.5 equivalent set 1.2.6 equal set 1.2.7 universal set
- 3. SET SET 1.1 DEFINITION 1.1 DEFINITION In Maths , sets are a collection of well - In Maths , sets are a collection of well - defined objects or elements. A set is defined objects or elements. A set is represented by a capital letter symbol. represented by a capital letter symbol.
- 4. 1.1.1 EXAMPLES OF SET SET OF ANIMALS SET OF FRUITS SET OF VEGETABLES
- 6. 1.2 TYPES OF SETS There is a very special set of great interest: the empty collection! Why should one care about the empty collection?Consider the set of solutions to the equation x^2+1=0. It has no elements at all in the set of Real numbers. Also consider all rectangles with one angle greater than 90 degrees. There is no such rectangle and hence this describes an empty set. So, the empty set is important, interesting and deserves a special symbol too.
- 7. 1.2.1 EMPTY SET OR NULL SET A set consisting of no elements is called the empty set or null set or void set. It is denoted by {}.
- 8. 1.2.2 SINGLETON SET A Set which has only one element is called a singleton set. eg: The set of all even prime numbers.
- 9. 1.2.3 FINITE SET A Set with finite number of elements is called finite set. eg: The set of family, the set of indoor/outdoor games you play, the set of curricular subjects you learn in school
- 10. 1.2.4 INFINITE SET A Set which is not finite is called as infinite set. eg: The set of all points on a line, {5,10,15,...}
- 11. 1.2.5 EQUIVALENT SET Two finite sets A and B are said to be equivalent if they contain the same number of elements. It is written as A=B If A and B are equivalent sets, then n(A)=n(B) eg; A= {ball, bat} B= {history, geography} here A is equivalent to B because n(A)=n(B) = 2
- 12. 1.2.6 EQUAL SET Two sets are said to be equal if they contain exactly the same elements, otherwise they are said to be unequal. In other words, two sets A and B are said to be equal, if (i) every element of A is also an element of B (ii) every element of B is also an element of A eg: A= {1,2,3,4} and B= {4,2,3,1} Since A and B contain exactly the same elements, A and B are equal sets.
- 13. 1.2.7 UNIVERSAL SET An Universal set is a set which contains all the elements of all sets under consideration and is usually denoted by U. eg: (i) If we discuss about the elements in Natural numbers, the the Universal set U is the set of all Natural numbers, U= {x : x ∈ N} (ii) If A= {Earth, Mars, Jupiter}, then the universal set U is the planets of the solar system.
- 14. 1.2.8 SUBSET Let A and B be two sets. If every elements of A is also an element B, the A is called a Subset of B, we write A ⊆ B. A ⊆ B is read as "A is a subset of B" Thus A ⊆ B, if a ∈ A implies a ∈ B If A is not a subset of B, we write A ⊄ B Clearly, if A is a subset of B then n(A) ≤ n(B) Since every element of A is also an element of B, the set B must have at least as many elements as a, thus n(A) ≤ n(B). The other way is also true. Suppose that n(A) > n(B), then A has more elements than b, and hence there is at least one element in A that cannot be in B, so A is not a subset of B. eg: (i) {1}⊆{1,2,3} (ii) {2,4} ⊄ {1,2,3}