111.

Let U ={1,2,3,4,5,6,7,8,9}

A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6}

Find (a) A' (b) B' (c)(A ∪ C)' (d) (A ∪ B)' (e) (A')' (f) (B-C)'

Fill in the blanks to make each of the following a true statement : (i) A ∪ A′ = . . . (ii) φ′ ∩ A = . . . (iii) A ∩ A′ = . . . (iv) U′ ∩ A = . . .

Id U = {1, 2, 3, 4, 5, 7, 8, 9}, A = {2, 4, 6, 8}  , B ={2, 3, 5, 7} verify De Morgan's laws:

Taking the set of natural numbers as the universal set, write down the complements of the following sets :

(i) {x : x is an even natural number}           (ii) {x : x is an odd natural number}

(iii) {x : x is a positive multiple of 3}            (iv) {x : x is a prime number}

(v) {x : x is a natural number divisible by 3 and 5}  

(vi) {x : x is a perfect square}                  (vii) {x : x is a perfect cube}

(viii) { x : x + 5 = 8 }                               (ix) { x : 2x + 5 = 9}

(x) { x : x ≥ 7 }                                       (xi) {x : x ∈ N and 2x + 1 > 10}

Prove that  : 

or 

For any two sets A  and B, prove that A' - B' = B - A.