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Using set theory, find the number of teachers who teach both Biology and Chemistry, given information about total teachers and those teaching each subject individually and in combination.

Mathematics

ScanSolve AI Answer

Let CC be the set of teachers who teach Chemistry, BB for Biology, and GG for Geography.
We are given the following information:

  • Total number of teachers, N=150N = 150.
  • Number of teachers who teach Chemistry, n(C)=61n(C) = 61.
  • Number of teachers who teach Biology, n(B)=65n(B) = 65.
  • Number of teachers who teach Geography, n(G)=45n(G) = 45.
  • Number of teachers who teach Biology and Chemistry but not Geography, n(B∩C∩G′)=25n(B \cap C \cap G') = 25.

The question asks for the number of teachers who teach both Biology and

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