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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is [UPSEAT 1990]

    A) 6

    B) 9

    C) 7

    D) All of these

    Correct Answer: D

    Solution :

    n(M) = 23, n(P) = 24, n= 19 n(M Ç P) = 12, n(M Ç C)= 9, n(P Ç C)= 7 n(M Ç P Ç C) = 4 We have to find n(M Ç P¢ Ç C¢), n(P  Ç M ¢ Ç C¢ ), n ( C Ç M ¢ Ç P ¢) Now n (M Ç P¢ Ç C¢) = n[M Ç (P È C)¢] = n(M)- n(M Ç (P È C)) = \[n(M)-n[(M\cap P)\cup (M\cap C)]\] = n(M) - n(M Ç P)- n(M Ç C) + n(M Ç P Ç C) = 23 -12 - 9 + 4 = 27 -21 = 6 n(P Ç M¢ Ç C¢) = n[P Ç (M È C)¢] = n(P)- n[P Ç (M È C)] = \[n(P)-n[(P\cap M)\cup (P\cap C)]\] = n(P) - n(P Ç M) - n(P Ç C) + n(P Ç M Ç C) = 24 - 12 - 7 + 4 = 9 \[n(C\cap {M}'\cap {P}')=n(C)-n(C\cap P)-n(C\cap M)+n(C\cap P\cap M)\]            = 19 - 7 - 9 + 4 = 23 - 16 = 7.


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