Question

in a fraternity with 33 members, 18 take mathematics, 5 take both mathematics and literature, and 8 take neither mathematics nor literature. how many take literature, but not mathematics? members take literature, but not mathematics.

Explanation:

Step1: Find the number of members in the universe

Let the total number of members in the fraternity be \(N\). We know that the number of members who take neither mathematics nor literature is 8. Let the number of members who take mathematics be \(M = 18\), the number of members who take both mathematics and literature be \(B=5\), and the total number of members in the fraternity be \(N = 33\).

Step2: Use the principle of set - theory

The number of members who take only mathematics is \(M - B=18 - 5 = 13\).
The number of members who take either mathematics or literature or both is \(N - 8=33 - 8 = 25\).
Let the number of members who take only literature be \(L\). We know that \(25=(M - B)+B + L\). Substituting the known values, we get \(25 = 13+5+L\).

Step3: Solve for the number of members who take only literature

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The number of members who take literature but not mathematics is 7.

Answer:

7