Use the Venn diagram to find each of the following.(A∪B)′(A\cup B)^{\prime}

(A∪B)′={0}(A\cup $$B)^{\prime}$$=\left\lbrace0\right\rbrace

Use the Venn diagram to find each of the following. ( A ∪ B ) ′ (A\cup B)^{\prime}

Welcome back. For this problem, we'd like to use the Venn diagram to find a union B complements. We'll be starting inside the parentheses with a union B. Now, we know that a union B is the set of everything just in A, just in B, or in both. So that would be in here, where we have the stuff just in A, in here, where we have the stuff just in B, and in here, where we have the stuff in both A and B. Now, we want to take the complement of a union B, which is everything inside of the universal set, but not in a union B. So, that's gonna be this region here, inside of our box for the universal set, but not inside either of our circles. As our circles contain the regions of A union B. So now we have that the region highlighted in yellow is a union B complement. That means that the elements of a union B complement are going to be the elements inside of that shaded region. We can see that the only element here is 0, so we can say that a union B complement is just the set containing 0. Great work.