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Cardinal NumberThe cardinal number of set V is the number of distinct element in it and is denoted by n(V).For example The vowels in the word DIFFERENTIATE are I, E, E, I, A and E. If we represent the set of vowels in the word DIFFERENTIATE in roster form we have : P = { I, E, A} Thus, even thought there are 6 vowels in the word, there are only 3 distinct elements in the set V. So, cardinalnumber n(P) = 3. Examples : 1) What is the cardinalnumber of set A of the composite numbers between 10 and 20? Solution : A = { 12,14,15,16,18} As there are 5 elements in set A. n(A) = 5. 2) If set C = { x  x is neither a prime nor a composite number}.Find n(C) Solution : C = { x  x is neither a prime nor a composite number} C = {1} ∴ n(C) = 1 3) If J = { 101, 103, 105,107,109}. Find n(J). Solution : J = { 101, 103, 105,107,109} n(J) = 5 4) If B ={ x x is a letter in the word PENINSULA}. Find n(B). Solution : B ={ x x is a letter in the word PENINSULA} B = { P, E, N, I, S, U, L, A} n(B) = 8 5) If E = { a,f,k,p,u,z }. Find n(E). solution : E = { a,f,k,p,u,z } n(E) = 6 6) If Q= { x 3 < x < 4}. Find n(Q). Solution : Q= { x x ∉ N3 < x < 4} As there is no element between 3 and 4. n(Q) = 0 n(Q) = Φ Set Theory • Sets • Representation of Set • Cardinal Number • Types of Sets • Pairs of Sets • Subset • Complement of Set • Union of the Sets • Intersection of Sets • Operations on Sets • De Morgan's Law • Venn Diagrams • Venndiagrams for sets • Venndiagrams for different situations • Problems on Intersection of Two Sets • Problems on Intersection of Three Sets
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