Set theory Chapter 1( class 11)

  1) Here Associative law of sets is used in the property form as xu(x'uy') is same as (xux')u y' for example 2*(3*5) => 30 and it can also be written as (2*3)*5 => 30 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)

  1)  2) Formula for  n (A ∪ B ∪ C)  = n(A ) + n ( B ) + n (C) – n ( A ∩ B) – n ( B ∩ C) – n ( C ∩ A) + n (A ∩ B ∩ C)

  1) 2)  If A is a set ,then the total number of subsets of A = 2 ⁿ⁽ᴬ⁾ 3) Proper Subset =( Total number of subsets - 1)  (or 2^n -1) for example in the above example the total subset is 8 , therefore proper subset is = 8-1 i,e 7. 4) 5) 6) 7) 8) 9) 10) 11) Also n(AΔB) = n(A) + n(B) - 2n(A⋂B) This formula is also important. 12) n(AUB) = n(A)+n(B) - n(A∩B) 13)

  1) Laws of Complement: 2) Venn-diagram proof: 3) Laws of intersection and Union (distributive law) 4) Venn-diagram proof: 5) Some NCERT sums:

  1) Addition theorem of two sets Here we notice that n(A) + n(b) => 5+6 = 11   this is so because there are some elements that are common to both A and B  but in AUB we count the common elements only "one" time , so  n(AUB) =9  Hence we infer that n(AUB) = n(A) + n(b) - n(A∩B),  1,2,3,4,5 is already counted in n(A) and therefore should be subtracted when counting n(B) or else it will be counted 2 times. 2) Addition theorem on 3 sets and n sets: 3) Some Problems on Addition theorem: