1th B.Com
Cartesian Product of Sets
The Cartesian products of sets mean the product of two non-empty sets in an ordered way. Or, in other words, the collection of all ordered pairs obtained by the product of two non-empty sets. An ordered pair means that two elements are taken from each set.
For two non-empty sets (say A & B), the first element of the pair is from one set A and the second element is taken from the second set B. The collection of all such pairs gives us a Cartesian product.
The Cartesian product of two non-empty sets A and B is denoted by A × B. Also, known as the cross-product or the product set of A and B. The ordered pairs (a, b) is such that a ∈ A and b ∈ B. So, A × B = {(a,b): a ∈ A, b ∈ B}. For example, Consider two non-empty sets A = {a1, a2, a3} and B = {b1, b2, b3}
Cartesian product A×B = {(a1,b1), (a1,b2), (a1,b3), ( a2,b1), (a2,b2),(a2,b3), (a3,b1), (a3,b2), (a3,b3)}.
It is interesting to know that (a1,b1) will be different from (b1,a1). If either of the two sets is a null set, i.e., either A = Φ or B = Φ, then, A × B = Φ i.e., A × B will also be a null set
Thank you
sanjeevan
23ucm029
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