1. **Problem Statement:** We have a Venn diagram representing staff members in an organization with total $S=1000$. The diagram shows two sets: Male and Married. 2. **Given Information:** - Total staff $S=1000$ - Male only: $100 + x$ - Both Male and Married (overlap): $x$ - Married only: $350$ - Outside both sets (neither Male nor Married): $2$ 3. **Step 1: Find $x$** The total number of staff is the sum of all regions: $$100 + x + x + 350 + 2 = 1000$$ Simplify: $$100 + 2x + 350 + 2 = 1000$$ $$452 + 2x = 1000$$ Subtract 452 from both sides: $$2x = 1000 - 452$$ $$2x = 548$$ Divide both sides by 2: $$x = \cancel{\frac{2x}{2}}{\frac{548}{2}} = 274$$ 4. **Step 2: Find number of female staff members** Female staff are those not in Male set. Total staff minus Male staff: Male staff = Male only + overlap = $(100 + x) + x = 100 + 274 + 274 = 648$ Female staff = $1000 - 648 = 352$ 5. **Step 3: Find number of married female staff** Married staff total = Married only + overlap = $350 + 274 = 624$ Married male staff = overlap = $274$ Married female staff = Married total - Married male = $624 - 274 = 350$ 6. **Step 4: Find number of single male staff** Single male staff = Male only = $100 + x = 100 + 274 = 374$ 7. **Step 5: Find number of staff who are male or married** Use formula for union: $$|Male \cup Married| = |Male| + |Married| - |Male \cap Married|$$ $$= 648 + 624 - 274 = 998$$ 8. **Step 6: Find percentage of single female staff** Single female staff = Female total - Married female = $352 - 350 = 2$ Percentage single female = $$\frac{2}{1000} \times 100 = 0.2\%$$ **Final answers:** - $x = 274$ - Female staff = 352 - Married female staff = 350 - Single male staff = 374 - Male or Married staff = 998 - Percentage single female = 0.2%