Given three sets . Prove that if we take a union and intersect it with the set , we will get the same set as if we took a union of and . Essentially, prove that .
and are three sets. Prove that if we take an intersection and unite it with the set , we will get the same set as if we took an intersection of two unions and . Essentially, prove that . Draw a Venn diagram for the set .
Let and be three sets. Prove that if we take an intersection and intersect it with the set , we will get the same set as if we took an intersection of with . Essentially, prove that it does not matter where to put the brackets in . Draw a Venn diagram for the set .
Prove the same for the union .