. Cartesian Product Illustration Let us consider the following two sets. A is the set of vegetables and B is the set of fruits. That is, A = {carrot, brinjal, ladies finger} and B = {apple, orange, grapes, strawberry} What are the possible ways of choosing a vegetable with a fruit?
(Fig. . ) Vegetables (A) Fruits (B) Carrot ( c ) Apple ( a ) Brinjal ( b ) Orange ( o ) Ladies finger ( l ) Grapes ( g ) Strawberry ( s ) We can select them in distinct pairs as given below. ( c , a ), ( c , o ), ( c , g ), ( c , s ), ( b , a ), ( b , o ), ( b , g ), ( b , s ), ( l , a ), ( l , o ), ( l , g ), ( l , s ) This collection represents the cartesian product of the set of vegetables and set of fruits.
Definition If A and B are two non-empty sets, then the set of all ordered pairs ( a , b ) such that Î , b Î is called the Cartesian Product of A and B , and is denoted by A ´ Thus, A ´ ∈ ∈ {( , ) | } a b A b B (read as A cross B). Also note that A × f = f Fig. . l Vegetables Fruits Fig.
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