Subjects set theory

Wedding Venn D55F73

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1. **State the problem:** We have a Venn diagram showing guests who had ice cream, custard, both, or neither at a wedding. The numbers are: - Ice Cream only: 51 - Custard only: 34 - Both Ice Cream and Custard: 9 - Neither: 13 We need to find: (a) How many guests had custard? (b) How many guests had both ice cream and custard? (c) How many guests went to the wedding? 2. **Formula and rules:** - Total who had custard = Custard only + Both - Total guests = Ice Cream only + Custard only + Both + Neither 3. **Calculate (a) number of guests who had custard:** $$\text{Custard} = 34 + 9 = 43$$ 4. **Calculate (b) number of guests who had both ice cream and custard:** Given directly as $$9$$. 5. **Calculate (c) total number of guests:** $$\text{Total} = 51 + 34 + 9 + 13 = 107$$ **Final answers:** (a) 43 (b) 9 (c) 107