Let `A= {1, 2, 3}`, `B = {3, 4}`and `C = {4, 5, 6}`. Find(i) `A xx(B nnC)` (ii) `(A xxB) nn(A xxC)`(iii) `A xx(B uuC)` (iv) `(A xxB) uu(A xxC)`

Explanation

(i) `BcapC={4}`
`A times (B cap C)={(1,4),(2,4),(3,4)}`
(ii) `A times B ={(1,3), (1,4), ((2,3),(2,4),(3,3),(3,4) }`
`A times C ={(1,4),(1,5),(1,6),(2,4),(2,5),(2,6), (3,4), (3,5), (3,6)}`
`( A times B) cap (A times C)={(1,4),(2,4),(3,4)}`
(iii) `B cup C ={3,4,5,6} `
`A times (bcup C) ={(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6)} `
(iv) `A times B={(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)}`
` A times C={(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)}`
`(A times B ) cup (A times C)= {(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6)}`