In the previous post we have discussed about Differential Calculus and In today's session we are going to discuss about Cartesian Product. An ordered pair, usually denoted by (x , y) is pair of elements x and y of some sets. Like the Cartesian product of two sets A and B is set of those pairs whose first co coordinate is an element of A and second co-ordinate is an element B. The set is denoted by A x B and is read as ‘A cross B’ or ‘product set of A and B’. Basically these sets are work as ordered pair usually denoted by (x, y) is a pair of element x and y of some sets, which is ordered in the sense that (x, y) ≠ (y, x) whenever x≠y. Here x is called first co-ordinate and y is called second co-ordinate of the ordered pair (x, y), for example ordered pair (1, 2) and (2, 1) consist of same element 1 and 2 but they are different because they represent different points in the co-ordinate plane. (know more about Cartesian Product, here)
Now we use this concept in Cartesian product as following manner:
A x B = (x, y): xϵ A Ʌ yϵ B, A and B are different sets which are multiplying with each other.
Let the value of set A = 1, 2, 3 and the value set B=3, 5;
A x B=1, 2, 3 x 3, 5;
=(1, 3), (1, 5), (2, 3), (2, 5), (3, 3), (3, 5) (Here we get many ordered pair of A x B which are called Cartesian product value of A x B),
And B x A=(3, 1), (3, 2), (3, 3), (5, 1), (5, 2), (5, 3) (Here we get many ordered pair of B x A which are called Cartesian product value of B x A ),
A x B ≠ B x A (it means both product are not same).
Similarly, we can define Cartesian product for n sets A1, A2, A3 …….An
A1, A2, A3 …….An = ( x1, x2, x3 …….xn ) x1 ϵ A1 É… x2ϵ A2 É… x3ϵ A3 ……………. É… xnϵ An
The element (x1, x2, x3 …….xn ) is called as n-type elements.
In this way we can solve the all Cartesian product problem.
Now we discuss what is Logarithmic Differentiation? We know exponent expression is defined as in the power expression like if y = ax, where x is logarithmic of y to the base a, in this case we will use the logarithmic differentiation. ISEET Physics syllabus helps students for their better study.
Now we use this concept in Cartesian product as following manner:
A x B = (x, y): xϵ A Ʌ yϵ B, A and B are different sets which are multiplying with each other.
Let the value of set A = 1, 2, 3 and the value set B=3, 5;
A x B=1, 2, 3 x 3, 5;
=(1, 3), (1, 5), (2, 3), (2, 5), (3, 3), (3, 5) (Here we get many ordered pair of A x B which are called Cartesian product value of A x B),
And B x A=(3, 1), (3, 2), (3, 3), (5, 1), (5, 2), (5, 3) (Here we get many ordered pair of B x A which are called Cartesian product value of B x A ),
A x B ≠ B x A (it means both product are not same).
Similarly, we can define Cartesian product for n sets A1, A2, A3 …….An
A1, A2, A3 …….An = ( x1, x2, x3 …….xn ) x1 ϵ A1 É… x2ϵ A2 É… x3ϵ A3 ……………. É… xnϵ An
The element (x1, x2, x3 …….xn ) is called as n-type elements.
In this way we can solve the all Cartesian product problem.
Now we discuss what is Logarithmic Differentiation? We know exponent expression is defined as in the power expression like if y = ax, where x is logarithmic of y to the base a, in this case we will use the logarithmic differentiation. ISEET Physics syllabus helps students for their better study.
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