1. Cartesian Product :
The Cartesian product of two sets `A, B` is a non-void set of all ordered pairs `(a, b)`,
where `a in A` and `b in B`. This is denoted by `A xx B`
`:.` `A xx B` = { `(a,b) | a in A` and `b in B` }
e.g. `A = { 1 ,2 } , B = {a,b}`
`A xx B = {(1,a) ,(1,b) ,(2,a),(2,b) }`
Note: (i) `A xx B ne B xx A` (Non-commutative)
(ii) `n (A xx B) =n (A) n (B) ` and `n( P (A xx B)) = 2^(n (A) n(B) )`
(iii) `A = phi` and `B= phi <=> A xx B = phi`
(iv) If `A` and `B` are two non-empty sets having n elements in common then `(Ax B)` and `(B x A)` have
`n^2` elements in common.
(v) `A xx ( B cup C ) = (A xx B) cup (A xx C)`
(vi) `A xx (B cap C) = (A xx B) cap ( A xx C)`
(vii) `A xx (B -C) = (A xx B) - (A xx C)`
1. Cartesian Product :
The Cartesian product of two sets `A, B` is a non-void set of all ordered pairs `(a, b)`,
where `a in A` and `b in B`. This is denoted by `A xx B`
`:.` `A xx B` = { `(a,b) | a in A` and `b in B` }
e.g. `A = { 1 ,2 } , B = {a,b}`
`A xx B = {(1,a) ,(1,b) ,(2,a),(2,b) }`
Note: (i) `A xx B ne B xx A` (Non-commutative)
(ii) `n (A xx B) =n (A) n (B) ` and `n( P (A xx B)) = 2^(n (A) n(B) )`
(iii) `A = phi` and `B= phi <=> A xx B = phi`
(iv) If `A` and `B` are two non-empty sets having n elements in common then `(Ax B)` and `(B x A)` have
`n^2` elements in common.
(v) `A xx ( B cup C ) = (A xx B) cup (A xx C)`
(vi) `A xx (B cap C) = (A xx B) cap ( A xx C)`
(vii) `A xx (B -C) = (A xx B) - (A xx C)`