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(D) Let $M, P,$ and $C$ represent the sets of students studying Mathematics,Physics,and Chemistry,respectively.Given: $n(M) = 23, n(P) = 24, n(C) = 19

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$22$

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(D) Let $M, P,$ and $C$ represent the sets of students studying Mathematics,Physics,and Chemistry,respectively.Given: $n(M) = 23, n(P) = 24, n(C) = 19, n(M \cap P) = 12, n(M \cap C) = 9, n(P \cap C) = 7, n(M \cap P \cap C) = 4$.To find the number of students who have taken exactly one subject,we calculate:$1$. Exactly Mathematics: $n(M) - [n(M \cap P) + n(M \cap C) - n(M \cap P \cap C)] = 23 - [12 + 9 - 4] = 23 - 17 = 6$.$2$. Exactly Physics: $n(P) - [n(P \cap M) + n(P \cap C) - n(M \cap P \cap C)] = 24 - [12 + 7 - 4] = 24 - 15 = 9$.$3$. Exactly Chemistry: $n(C) - [n(C \cap M) + n(C \cap P) - n(M \cap P \cap C)] = 19 - [9 + 7 - 4] = 19 - 12 = 7$.The total number of students who have taken exactly one subject is $6 + 9 + 7 = 22$.

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