Complement of a Set

Venn diagram,Union and intersection and complement of sets and their algebraic properties

If A ={1,2,3,4} and U={1,2,3,4,5,6,7,8} is universal set, then write the complement of set A .

(a) The Complement of the union of two sets is the intersection of their complements and the complement of the intersection of two sets is the union of their complements.These are called De Morgan's Law.Prove any one of the above two laws by Venn diagram (use colour pencil,scale,"],[" etc...) (b) Verify any one of the De Morgan's Law for U={1,2,3,4,5,...8,9,10}A={2,3,5,7,9,10}B={1,3,5,8,10}

|X| represent number of elements in region X. Now the following conditions are given |U|=14, |(A-B)^(C)|=12, |A cup B|=9 |A triangle B|=7, Where A and B are two subsets of the universal set U and A^(c) represents complement of set A, then

If X and Y are two sets and X' denotes the complement of X then Xcap(XuuY) is equal to :