Mathematics Relations

Cartesian Product of two sets :

Let `A` and `B` be any two non empty sets. The set of all ordered pairs `(a, b)` such that `a in A` and `b in B` is called as cartesian product of

sets `A` and `B` and is denotes by `A xx B.`

The cartesian product of two sets `A, B` is a non-void set of all ordered pairs `(a, b).`

`A = {1 , 2, 3}; B = {p, q, r}`

`A xx B = {(a, b) // a in A` and `b in B}`

`= {( 1, p), (1 , q), (1 , r), (2 , p), (2 , q), (2 , r), (3 , p), (3 , q), (3 , r)}`

Total number of Relation from `A` to `B:`

Let number of relations from `A` to `B` be `x.`

Let `A` contain `m` elements and `B` contain `n` element's.

Number of e lement's in `A xx B -> mxx n`

Number of non void subset's `= text()^(mn)C_1 + text()^(mn)C_2 + text()^mnC_(mn) = 2^(mn)-1`


 
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