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In a certain examination, 52 candidates offered biology, 60 history, 96 offered mathhematics , 21 offered biology and history, 22 offered both biology and mathematics, 16 mathematics and history. If 7 candidates offer all the three subjects find:(a) how many candidates were there for the examination

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2 answers

  1. number(biology OR history OR mathematics) =
    number(biology) + number(history) + number(math) - number(history ANS biology) - number(history AND math) - number(biology AND math) + number(biology AND history AND mathematics)

    you are given each of those values, just plug in and evaluate.

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  2. Using what you know about the intersections of sets, and using a Venn diagram, you can see that
    (52+60+96)-(21+22+16)+(7) = 156

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