Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Ordered pairs & Cartesian Product

Ordered Pairs:

If  \{a, b\} is a set consisting of elements  a, b ( a may be equal to  b ), it is called pair, where  a be the 1st component and  b be the second component, then we call  \{a, b\} be ordered pair and written as  (a, b) .

 \rightarrow (a,b)\neq (b,a) (\forall a\text { and } b)

 \rightarrow (a,b) = (c,d) \text { iff } a =c, b=d

Cartesian Product:

If  A,B are non-empty sets, then their Cartesian product, denoted by  A \times B i.e.,  A \times B = \{(a ,b): a \in A , b\in B \}

\rightarrow A \times B \neq B \times A

\rightarrow The product  R \times R is known as Cartesian Plane.

\rightarrow  R \times R \times R= R^3 is three dimensional space.

\rightarrow A_1, A_2,…,A_n be  n non-empty sets, where {(x_1,x_2,…,x_n): x, \in A_1, x_2 \in A_2,…,x_n\in A_n } is element of  A_1 \times A_2\times … \times A_n

 (x_1,x_2,…, x_n) is known as  n– tuples.

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