Emaths All about Mathematics

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OPERATIONS ON SETS

(1) Union of Sets: The union of two sets A and B is the set of all the elements which are either in A or in B or in both A and B. It is denoted by . Let (2) Intersection of Sets: The intersection...

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LAWS OF SET OPERATIONS

(1) Idempotent laws : (2) Identity laws: (3) Commutative laws: (4) Associative laws: (5) Distributive Laws: (6) De-Morgan’s Laws:

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CARDINAL NUMBER OF SETS

Some important results derived from Venn diagrams are as follows: A, B and C are three sets. A and B are disjoint sets.

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VENN DIAGRAM

The pictorial representation of sets is called Venn diagram. The universal set is represented by a rectangular region and its subsets by circles inside the rectangle. In the above given Venn diagram, and and .   Here,and . If, there is no common elements in...

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INTERVALS

(1) Closed Interval: Let a and b are two given real numbers such that , then (2) Open Interval: Let a and b are two given real numbers such that then or (3) Closed-open Interval: Let a and b are two given real numbers such...

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SUBSETS

SUBSET: A set P is said to be a subset of a set Q if each element of P is also an element of Q. If P is subset of Q, we write PROPER SUBSET: If and then P is called a proper subset of...

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RADIUS AND CENTRE OF CIRCLE

If the equation of circle is Then center = (–g, –f) and radius                   Or If the equation of circle is  By completing square,                                                         Example1: Find the centre and radius of the circle Solution: Comparing the given equation with the standard equation,  ...

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DISTANCE FROM A POINT TO THE GIVEN LINE

Consider a point P(x1, y1) and a line in the line co – ordinate axes. The coordinates of points A and B are and . Area of   Example: Find the distance from the point (1, 2) to the line .   The required distance...