1. **State the problem:** We have a squash club with 27 members. - 19 members have black hair. - 14 members have brown eyes. - 11 members have both black hair and brown eyes. (i) We want to represent this on a Venn diagram. (ii) Using this, we find: I. The number of members with black hair or brown eyes. II. The number of members with black hair but not brown eyes. 2. **Venn diagram construction:** - Let set $B$ be members with black hair. - Let set $E$ be members with brown eyes. - We know the intersection $|B \cap E| = 11$. 3. **Calculate black hair only:** $$|B \setminus E| = |B| - |B \cap E| = 19 - 11 = 8$$ 4. **Calculate brown eyes only:** $$|E \setminus B| = |E| - |B \cap E| = 14 - 11 = 3$$ 5. **Calculate members with either black hair or brown eyes:** Using the inclusion-exclusion principle: $$|B \cup E| = |B| + |E| - |B \cap E| = 19 + 14 - 11 = 22$$ 6. **Calculate members with black hair but not brown eyes:** This is the black hair only group calculated in step 3: $$8$$ **Final answers:** I. Number of members with black hair or brown eyes = $22$ II. Number of members with black hair but not brown eyes = $8$