Please with the venn diagram

We have two sets, Mathematics ($M$) and Science ($S$), within a universal set of students ($U$).

\begin{tikzpicture} \begin{scope} \clip (0,0) circle (1.5cm); \fill[gray!20] (1,0) circle (1.5cm); \end{scope} \draw (0,0) circle (1.5cm) node[left] {$M$}; \draw (1,0) circle (1.5cm) node[right] {$S$}; \draw (-2,-2) rectangle (3,2) node[above left] {$U$}; % Labels for regions \node at (0.5,0) {8}; % M intersect S \node at (-0.7,0) {x}; % M only \node at (1.7,0) {y}; % S only \end{tikzpicture}

• Total students, $|U| = 25$.
• Students who passed Science, $|S| = 17$.
• Students who passed both Mathematics and Science, $|M \cap S| = 8$.

We place the number of students who passed both Mathematics and Science in the intersection of the two circles:

$$|M \cap S| = 8$$

The total number of students who passed Science is 17. Since 8 of them also passed Mathematics, the number of students who passed only Science is:

$$|S \text{ only}| = |S| - |M \cap S| = 17 - 8 = 9$$

We place this value in the part of the Science circle that does not overlap with Mathematics.

\begin{tikzpicture} \begin{scope} \clip (0,0) circle (1.5cm); \fill[gray!20] (1,0) circle (1.5cm); \end{scope} \draw (0,0) circle (1.5cm) node[left] {$M$}; \draw (1,0) circle (1.5cm) node[right] {$S$}; \draw (-2,-2) rectangle (3,2) node[above left] {$U$}; % Labels for regions \node at (0.5,0) {8}; % M intersect S \node at (-0.7,0) {x}; % M only \node at (1.7,0) {9}; % S only \end{tikzpicture}

The problem implies that all 25 students passed at least one subject (no students passed neither). So, the sum of students in all three regions of the Venn diagram (only M, only S, both M and S) must equal the total number of students.
Let $x$ be the number of students who passed only Mathematics.

$$|U| = |M \text{ only}| + |S \text{ only}| + |M \cap S|$$ $$25 = x + 9 + 8$$ $$25 = x + 17$$ $$x = 25 - 17$$ $$x = 8$$

So, 8 students passed only Mathematics.

\begin{tikzpicture} \begin{scope} \clip (0,0) circle (1.5cm); \fill[gray!20] (1,0) circle (1.5cm); \end{scope} \draw (0,0) circle (1.5cm) node[left] {$M$}; \draw (1,0) circle (1.5cm) node[right] {$S$}; \draw (-2,-2) rectangle (3,2) node[above left] {$U$}; % Labels for regions \node at (0.5,0) {8}; % M intersect S \node at (-0.7,0) {8}; % M only \node at (1.7,0) {9}; % S only \end{tikzpicture}

The total number of students who passed Mathematics includes those who passed only Mathematics and those who passed both Mathematics and Science.

$$|M| = |M \text{ only}| + |M \cap S|$$ $$|M| = 8 + 8$$ $$|M| = 16$$

The total number of students who passed Mathematics is $\text{16}$.