of students who play all the three games = 8 Solving Word Problem of students who play both (foot ball and cricket) only = 17 of students who play both foot ball and cricket = 25 of students who play both (hockey & cricket) only = 7
of students who play both hockey & cricket = 15 of students who play both (foot ball & hockey) only = 12 of students who play both foot ball & hockey = 20 Venn diagram related to the above situation :įrom the venn diagram, we can have the following details. Let F, H and C represent the set of students who play foot ball, hockey and cricket respectively. In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Total number of elements related to B only. Total number of elements related to both (A & C) only. Total number of elements related to both A & C Total number of elements related to both (B & C) only. Total number of elements related to both B & C Total number of elements related to both (A & B) only. Total number of elements related to both A & B Total number of elements related to C only. Total number of elements related to A only. N(C) = Total number of elements related to C. N(B) = Total number of elements related to B. N(A) = Total number of elements related to A. N(AuBuC) = Total number of elements related to any of the three events A, B & C. N(AuB) = Total number of elements related to any of the two events A & B. Let us come to know about the following terms in details. Then, n(A u B) = n(A) + n(B) + n(C) Addition Theorem on Sets
N(A u B u C) = n(A) + n(B) + n(C) - n(A n B) - n(B n C) - n(A n C) + n(A n B n C) If A and B are disjoint sets, n(A n B) = 0 In case, two or more sets are combined using operations on sets, we can find the cardinality using the formulas given below.
That is, there are 7 elements in the given set A. Here, n(A) stands for cardinality of the set A Cardinality of a set is a measure of the number of elements in the set.įor example, let A =
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