Of the members of three athletic teams in a s | vedclass

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Question

(A) Let $C, H, F$ denote the sets of members who are on the cricket team,hockey team,and football team respectively.We are given $n(C) = 21, n(H) = 26

Vedclass · Accepted Answer

$43$

Vedclass · Answer

(A) Let $C, H, F$ denote the sets of members who are on the cricket team,hockey team,and football team respectively.We are given $n(C) = 21, n(H) = 26, n(F) = 29$.Also,$n(H \cap C) = 14, n(H \cap F) = 15, n(F \cap C) = 12$ and $n(C \cap H \cap F) = 8$.We need to find the total number of members,which is $n(C \cup H \cup F)$.Using the principle of inclusion-exclusion:$n(C \cup H \cup F) = n(C) + n(H) + n(F) - n(C \cap H) - n(H \cap F) - n(F \cap C) + n(C \cap H \cap F)$$n(C \cup H \cup F) = (21 + 26 + 29) - (14 + 15 + 12) + 8$$n(C \cup H \cup F) = 76 - 41 + 8 = 43$.Thus,there are $43$ members in total.

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