Posts

Unit - 1, Sets

Image
Exercise - 1.1  1. a) Present the cardinality of sets with examples and show it to your teacher. Answer👉  Present the cardinality of sets with examples Cardinality refers to the number of elements in a set. For a set A A A , the cardinality is denoted as n ( A ) n(A) n ( A ) . Examples : If A = { 1 , 2 , 3 , 4 } A = \{1, 2, 3, 4\} A = { 1 , 2 , 3 , 4 } , then n ( A ) = 4 n(A) = 4 n ( A ) = 4 (4 elements). If B = { a , b , c } B = \{a, b, c\} B = { a , b , c } , then n ( B ) = 3 n(B) = 3 n ( B ) = 3 (3 elements). To present to your teacher, you can list these sets and their cardinalities clearly. b) Fortwo sets A and B, A c B, find the values of n(AUB) and n(AMB).  IFA and B are overlapping sets, state the formula for n(AUB). Answer👉  For two sets  A A A  and  B B B , if  A ⊆ B A \subseteq B A ⊆ B : Values of  n ( A ∪ B ) n(A \cup B) n ( A ∪ B ) : The union of two sets  A A A  and  B B B  combines all elements in both ...
Post a Comment
Read more

Unit -1 Part 2

Image
  Question 5 a) A survey was carried out among 900 people of a community: 525 people read  Madhupark . 450 people read  Yabamanch . 75 people didn’t read either of the newspapers. Subquestions: i) Show the information in a Venn diagram. We denote the sets: M M M : People who read Madhupark. Y Y Y : People who read Yabamanch. The total number of people in the universal set  U U U  is  900 900 900 . n ( M ∪ Y ) = n ( U ) − n ( neither ) = 900 − 75 = 825. n(M \cup Y) = n(U) - n(\text{neither}) = 900 - 75 = 825. n ( M ∪ Y ) = n ( U ) − n ( neither ) = 900 − 75 = 825. Let  x x x  be the number of people who read  both newspapers . n ( M ∪ Y ) = n ( M ) + n ( Y ) − n ( M ∩ Y ) . n(M \cup Y) = n(M) + n(Y) - n(M \cap Y). n ( M ∪ Y ) = n ( M ) + n ( Y ) − n ( M ∩ Y ) . Substitute the values: 825 = 525 + 450 − x    ⟹    x = 150. 825 = 525 + 450 - x \quad \implies \quad x = 150. 825 = 525 + 450 − x ⟹ x = 150. ii) Find the number of people who re...
Post a Comment
Read more