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Venn diagrams showing Distributive properties as well as Complements of union and intersection

# Venn diagrams showing Distributive properties as well as Complements of union and intersection

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1 Using Venn Diagrams to demonstrate the Distributive properties of the union, intersection and set complement operators Combining the union and intersection operators Property: Union is distributive over Intersection That is, given any sets A , B and C , A ( B C ) = ( A B ) ( A C ) To demonstrate this using Venn diagrams, we work our way up to diagrams depicting the sets cor- responding to each of the left and right sides of this equation, to see that we get the exact same set for each. Step 1 Left Hand Side set: We need to draw a Venn diagram showing the set A ( B C ). We start by drawing, separately, the sets A and ( B C ), and then use those diagrams to draw the union of those sets. When we take the union of sets shaded in different Venn diagrams, we use (i.e., shade) all parts of the final diagram which are shaded in either of the two diagrams. A C B A C B A C B Figure 1(a): Figure 1(b): Figure 1(c) Set A. The subset B C . A ( B C ) is everything which is shaded in 1(a) or 1(b).

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Venn diagrams showing Distributive properties as well as Complements of union and intersection

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