Note:
If A has m elements, B has n elements, then A x B has mn elements. (a,b) = (c,d) a = c and b = d (Equality of ordered pairs). 'a' is called the first entry or first component and 'b' is called the second entry or second componen..
If A has m elements, B has n elements, then A x B has mn elements. (a,b) = (c,d) a = c and b = d (Equality of ordered pairs). 'a' is called the first entry or first component and 'b' is called the second entry or second componen..Ordered Pairs, Equivalence relation
Ordered Pairs - An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order. Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, these numbers are sa..
Ordered Pairs - An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order. Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, these numbers are sa..Summary Relations and Functions
A pair of objects, written in a specified order is called an ordered pair . A pair of objects, written in a specified order is called an ordered pair . For the ordered pair (a,b), a is called the first element and b, the second element. The ordered pairs (a,b) and (c,d) ..
A pair of objects, written in a specified order is called an ordered pair . A pair of objects, written in a specified order is called an ordered pair . For the ordered pair (a,b), a is called the first element and b, the second element. The ordered pairs (a,b) and (c,d) ..One-one function (or an injective map)
A function f : A g B is called a 1-1 mapping, if every element of f(A) does not have more than one pre-image. ..
A function f : A g B is called a 1-1 mapping, if every element of f(A) does not have more than one pre-image. ..Ordered Pair An ordered pair has a pair of elements which occur in a definite order. If two ordered pairs (a, b) and (x, y) are equal, (a, b) = (x, y) then a = x, b = ..
An ordered pair has a pair of elements which occur in a definite order. If two ordered pairs (a, b) and (x, y) are equal, (a, b) = (x, y) then a = x, b = ..Summary Ordered Pairs and Cartesian Product
An ordered pair has a pair of elements which occur in a definite order. An ordered pair has a pair of elements which occur in a definite order. Cartesian Product - Given two sets A and B, all possible ordered pairs (x, y) obtained such that x A and y B is called the car..
3. Onto function
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..Many-one function
Every one element of A corresponds to more than one element of B. In example 3, one image has three pre-images. In example 4, one image has four pre-images. Therefore, many-one relations in examples 3 and 4 are many-one functions. Consider the following examples and note why th..
Every one element of A corresponds to more than one element of B. In example 3, one image has three pre-images. In example 4, one image has four pre-images. Therefore, many-one relations in examples 3 and 4 are many-one functions. Consider the following examples and note why th..Proof:
Let (a,b) be an arbitrary element of A x B. ..
Let (a,b) be an arbitrary element of A x B. ..Ordered Pairs and Cartesian Product
Ordered Pairs and Cartesian Product - In a Rectangular Cartesian System of coordinates the position of a point in a plane is determined by an ordered pair whose elements give the distances from the intersecting straight lines at right angles to each other. These lines are called the axes...
Ordered Pairs and Cartesian Product - In a Rectangular Cartesian System of coordinates the position of a point in a plane is determined by an ordered pair whose elements give the distances from the intersecting straight lines at right angles to each other. These lines are called the axes...See what our Users say :
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