1. **State the problem:** A squash club has 27 members. 19 have black hair, 14 have brown eyes, and some have both black hair and brown eyes. 2. **Identify given values:** - Total members, $N = 27$ - Members with black hair, $B = 19$ - Members with brown eyes, $E = 14$ - Members with both black hair and brown eyes, $B \cap E = x$ 3. **Place this information on a Venn diagram:** - The total number in the union of black hair or brown eyes sets is given by the principle of inclusion-exclusion: $$|B \cup E| = |B| + |E| - |B \cap E| = 19 + 14 - x = 33 - x$$ - Since the total club members is 27, we know that: $$|B \cup E| \leq 27$$ - From this, we have: $$33 - x \leq 27 \implies x \geq 6$$ Assuming the problem's intent is that the number with both black hair and brown eyes is 6 to fit total of 27 members. 4. **Answer (i):** On the Venn diagram, - Members with both black hair and brown eyes = 6 - Members with only black hair = $19 - 6 = 13$ - Members with only brown eyes = $14 - 6 = 8$ - Members with neither = $27 - (13 + 6 + 8) = 0$ 5. **Answer (ii):** Find the numbers requested: I. Number of members with black or brown eyes = $|B \cup E| = 13 + 6 + 8 = 27$ II. Number of members with black hair but not brown eyes = members with only black hair = $13$ **Final answers:** - (i) Venn diagram values: black hair only = 13, brown eyes only = 8, both = 6, neither = 0 - (ii) I. $27$ - (ii) II. $13$