मान लीजिए की `A = {1, 2, 3}, B = {3, 4}` और `C = {4, 5, 6}`, तो, निम्नलिखित के मान ज्ञात कीजिए:
(i) `A xx (B nn C)` (ii) `(A xx B) nn (A xx C)`
(iii) `A xx (B uu C)` (iv) `(A xx B) uu (A xx C)`

Explanation

`:' A = {1, 2, 3}, B = {3, 4}` तथा `C = {4, 5, 6}`
(i) `B nn C = {4}`
`:. A xx (B nn C) = {1, 2, 3} xx {4}`
`= {(1, 4), (2, 4), (3, 4)}`
(ii) `A xx B = {1, 2, 3} xx {3, 4}`
`={(1, 3), (2, 3), (3, 3), (1, 4),(2, 4), (3, 4)}`
`A xx C = {1, 2, 3} xx {4, 5, 6}`
`= {(1, 4), (2, 4), (3, 4), (1, 5), (3, 5), (3, 5), (1, 6), (2, 6), (3, 6)}`
`(A xx B) nn (A xx C) = {(1, 4), (2, 4), (3, 4)}`
(iii_ `B uu C = {3, 4} uu {4, 5, 6}`
`= {3, 4, 5, 6}`
`:. A xx (B uu C) = {1, 2, 3} xx {3, 4, 5, 6}`
`= {(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (1, 5), (2,5), (3,5), (1, 6), (2, 6), (3, 6)`
(iv) `A xx B = {(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4)}`
और `A xx C = {(1, 4), (2, 4), (3, 4), (1,5), (2,5), (3,5), (1, 6), (2, 6),(3, 6)}`
`:. (A xx B) uu (A xx C) = {(1,3), (2, 3), (3,3), (1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5), (1, 6), (2, 6), (3, 6)}`