# intersection of sets

5, 6, 7, 8} = {3, 4}, A First, let A be the set of the number of windows that represents "fewer than 6 windows". Thus: $C^c=\left\{x\mid x\ge3\right\} \nonumber$, $B\cap C^c=\left\{x\mid x<6\right\}\cap\left\{x\mid x\ge3\right\}=\left\{x\mid3\le x<6\right\} \nonumber$, $A\cup\left(B\cap C^c\right)=\:\left\{x\mid x>8\right\}\cup\left\{x\mid3\le x<6\right\} \nonumber$. If U is a universal set and X is any subset of U then the complement of X is the set of all elements of the set U apart from the elements of X. ∩ Intersection of sets A & B has all the elements which are common to set A and set BIt is represented by symbol ∩Let A = {1, 2,3, 4} , B = {3, 4, 5, 6}A ∩ B = {3, 4}The blue region is A ∩ BProperties of IntersectionA ∩ B = B ∩ A (Commutative law). In mathematics, the intersection of two or more objects is another, usually "smaller" object. Next, let B be the set of the number of units that represents "less than 18 units". Consider the following sentence, "Find the probability that a household has fewer than 6 windows or has a dozen windows." }, B ∪ C = {3, 4, 5, 6} ∪ {6, 7, 8} = {3, 4, 5, 6, 7, 8}, A ∩ (B ∪ C) = {1, 2, 6 3, 4 For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. The set operations are performed on two or more sets to obtain a combination of elements, as per the operation performed on them. An element is in the union of two sets if it is in the first set, the second set, or both. prove distributive law using Venn Diagram. Example: If A = {1,2,3,4,5,6,7} and B = {6,7} are two sets. The intersection of two sets A and B ( denoted by A∩B ) is the set of all elements that is common to both A and B. This is the set that contains the numbers from 1 through 17: $B=\left\{1,\:2,\:3,\:...,\:17\right\} \nonumber$. It is simply defined as the set containing all elements of the set A that also belong to the set B, and similarly all elements of set B belong to the set A. Example: If set A = {1,2,3,4} and B {6,7}, Then, Union of sets, A ∪ B = {1,2,3,4,6,7}. The number line below displays the answer: Suppose that we pick a person at random and are interested in finding the probability that the person's birth month came after July and did not come after September. Notice that the complement of "$$<$$" is "$$\ge$$". Write this in set notation. B = {1, 2, 3, 4} 1 Assuming that students only take a whole number of units, write this in set notation as the intersection of two sets and then write out this intersection. If two sets A and B are given, then the intersection of A and B is the subset of universal set U, which consist of elements common to both A and B. First, let A be the set of numbers of units that represents "more than 12 units".

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