Math 121 Week 6 Worksheet Venn Diagrams

Math 121 Week 6 Worksheet Venn Diagrams - (A∩B)′...

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Week 6 Worksheet Venn Diagrams 1) i) The sets A and B are disjoint so we should draw the Venn diagram as follows: 2) Draw a Venn diagram and number all the disjoint regions. Shade in the regions corresponding to (A∩B)′ and A B′ and they are both the same Venn diagram. In particular: (A∩B)′ = (region 2)′
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Unformatted text preview: (A∩B)′ = (region 2)′ = {x | x ∈ U and x ∉ region 2} = regions 1, 3, 4 A′ ∪ B′ = {x | x ∈ U and x ∉ A} ∪ {x | x ∈ U and x ∉ B} = (regions 3, 4) ∪ (regions 1, 4) = regions 1, 3, 4 So (A∩B)′ = A′ ∪ B′ , as they both correspond to regions 1, 3, and 4....
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