(a)  A' = U - A = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4} = {5, 6, 7, 8, 9}

(b) B' = U - B = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8} = {1, 3, 5, 7, 9}

(c)   =   

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)' 

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)'

∴ 

       = {7, 8, 9}

(d)    

 

                     = {5, 7, 9}

(e)       (A')' = A                                                                            (By involution  law)

         ∴    (A')' = A = {1, 2, 3, 4}

(f)    B - C = {2, 8}

∴       (B - C)' = U - (B - C) = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 8} = {1, 3, 4, 5, 6, 7, 9}

R-Q = Set of irrational numbers =

(a)    A' = U - A = {a,b,c,d,e,f,g,h} - {a, b, c} = (d, e, f, g, h}

(b) B' = U - B = {a, b, c, d, e , f, g, h} - {d, e, f, g} = {a, b, c, h}

(c) C ' = U - C = {a, b, c, d, e, f, g} - (a, c, e, g) = {b, d, f, h}

(d) D' = U - D = {a, b, c,, d, e, f, g, h} - {f, g, h, a} = {b, c, d, e}

U = Set of alll triangles = {x : x is a triangle}

A = Set  of all trinalges with at least one angle different 

= {x : x is a triangle and x has at least one angle different 

∴ A' = U - A

= {x : x is a triangle} - {x : x is a triangle and x at least one angle different }

= {x : x is a triangle and no angle is different }

= {x :x is a triangle and x has all angles equal }

= Set of equilateral triangles.

Hence, A' = Set of all equlateral triangles.