Let the universal set : U = { 1 , 2 , 3 , . . . , 10 } .Let A = { 1 , 4 , 7 , 10 }, B = { 1 , 2 , 3 , 4 , 5 }, and C = { 2 , 4 , 6 , 8 }. ?

1.
U'
= U - U
= ∅

2.
B ⋂ ∅
= B
= {1, 2, 3, 4, 5}

3.
B ⋂ U
= B
= {1, 2, 3, 4, 5}

4.
B' ⋂ (C - A)
= (U - B) ⋂ (C - A)
= ({1, 2, 3, ……, 10} - {1, 2, 3, 4, 5}) ⋂ ({2, 4, 6, 8} - {1, 4, 7, 10})
= {6, 7, 8, 9, 10} ⋂ {2, 6, 8}
= {6, 8}

5.
A' ⋂ B' ⋃ C
= (U - A) ⋂ {U - B} ⋃ C
= ({1, 2, 3, ……, 10} - {1, 4, 7, 10}) ⋂ ({1, 2, 3, ……, 10} - {1, 2, 3, 4, 5}) ⋃ {2, 4, 6, 8}
= {1, 2, 3, 5, 6, 8, 9} ⋂ {6, 7, 8, 9, 10} ⋃ {2, 4, 6, 8}
= {6, 8, 9} ⋃ {2, 4, 6, 8}
= {2, 4, 6, 8, 9}