1. **State the problem:** We have 800 households and three brands of cooking oils: Rina, Avena, and Elianto. Given data: - Total households: 800 - Used Rina: 230 - Used Avena: 245 - Used Elianto: 325 - Used all three: 30 - Used Rina and Elianto: 70 - Used Rina only: 110 - Used Elianto only: 185 2. **Find the number of households who used Rina and Avena but not Elianto:** Let this be $x$. 3. **Find the number of households who used Avena and Elianto but not Rina:** Let this be $y$. 4. **Calculate the number of households who used Rina and Elianto only:** Given as 70, but this includes those who used all three (30), so those who used only Rina and Elianto are $70 - 30 = 40$. 5. **Calculate the number of households who used Rina only:** Given as 110. 6. **Calculate the number of households who used Elianto only:** Given as 185. 7. **Calculate the number of households who used Rina:** Sum of Rina only, Rina and Avena only ($x$), Rina and Elianto only (40), and all three (30): $$110 + x + 40 + 30 = 230$$ Simplify: $$x + 180 = 230$$ $$x = 50$$ 8. **Calculate the number of households who used Elianto:** Sum of Elianto only, Avena and Elianto only ($y$), Rina and Elianto only (40), and all three (30): $$185 + y + 40 + 30 = 325$$ Simplify: $$y + 255 = 325$$ $$y = 70$$ 9. **Calculate the number of households who used Avena:** Sum of Avena only, Rina and Avena only (50), Avena and Elianto only (70), and all three (30): Let Avena only be $a$. $$a + 50 + 70 + 30 = 245$$ Simplify: $$a + 150 = 245$$ $$a = 95$$ 10. **Calculate the total number of households who used at least one brand:** Sum all exclusive and overlapping groups: $$110 + 50 + 40 + 95 + 70 + 185 + 30 = 580$$ 11. **Calculate the number of households who used none of the brands:** Total households minus those who used at least one brand: $$800 - 580 = 220$$ **Final answers:** - (i) The Venn diagram sets are: - Rina only: 110 - Avena only: 95 - Elianto only: 185 - Rina and Avena only: 50 - Avena and Elianto only: 70 - Rina and Elianto only: 40 - All three: 30 - (ii) Number of households who used none: 220