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 cartesian product of th..
Summary
Finding the solution by the method of substitution. (i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factor..
Corollary:
The function f : A g B is one-one and onto. ..
The function f : A g B is one-one and onto. ..Function Solved Examples
The arrow diagram represents a relation from set A to set B. (i) Represent the relation in roster form. (ii) Is this relation a function? Give reason for your answer. (i) {(1, 2), (2, 4), (5, 2), (3, 10), (4, 10)} (ii) Yes it is a function. Every first element is mapped and it is m..
More Solved Examples
The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its "input") and the other as secondary (the value of the function, or "o..
Linear equations in two variables
An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear.An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear. A linear equ..
An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear.An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear. A linear equ..Summary Relations and Functions
>Relation from a set A to a set B is a subset of A x B. - A relation R on a set A is reflexive if a R a, " a A- A relation R on a set A is symmetric if a R b b R a. - A relation R on a set A transitive if a R b and b R c a R c. A relation R is said to be an equivalence relation on A if it is reflex..
Proof:
Hence gof is one-one . c) If each f and g is also then so is gof. To prove gof is onto we have to prove that every element of u U is an image element for some x S under gof, since g is onto t T such that g(t) = u. gof(x) = g(f(x)) = g(t) =..
Hence gof is one-one . c) If each f and g is also then so is gof. To prove gof is onto we have to prove that every element of u U is an image element for some x S under gof, since g is onto t T such that g(t) = u. gof(x) = g(f(x)) = g(t) =..Simultaneous Equations
A linear equations in two variables x and y is of the form ax + by + c = 0 ( ) where a, b, c are real numbers. To find a solution for this equation, we can assign any value for one of the variables and find the value of the other variable such that the two sides of the equation are e..
A linear equations in two variables x and y is of the form ax + by + c = 0 ( ) where a, b, c are real numbers. To find a solution for this equation, we can assign any value for one of the variables and find the value of the other variable such that the two sides of the equation are e..Summary Simultaneous Equations
Finding the solution by the method of substitution. Finding the solution by the method of substitution. (i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factors. (ii) By addition or subtraction, this variable (x) ..
Result
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