Subjects set theory

Female Married F0C424

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1. **State the problem:** We need to find how many female staff members are married in the organization. 2. **Understand the Venn diagram:** - Total staff $S = 1000$ - Male only: $100 + x$ - Male and Married (overlap): $x$ - Married only (female married): $350$ - Outside both sets (neither male nor married): $2$ 3. **Find $x$ first:** Total staff is sum of all regions: $$100 + x + x + 350 + 2 = 1000$$ Simplify: $$100 + 2x + 350 + 2 = 1000$$ $$452 + 2x = 1000$$ Subtract 452: $$2x = 1000 - 452 = 548$$ Divide both sides by 2: $$2\cancel{x} = 548 \Rightarrow \cancel{2}x = 274$$ So, $$x = 274$$ 4. **Calculate female married:** Female married are those in the Married circle but not Male, which is the Married only region: $$350$$ 5. **Final answer:** The number of female staff members who are married is **350**.
S = 1000MaleMarried100 + 2742743502