While you may be dealing with functions and relations, understanding them in pictorial forms makes it rather easier. Mapping diagrams help in the clearer understanding of the relations of numbers in one set of values and the other set of values. Using Mapping Diagrams Mapping diagrams prove to be useful while you’re working with functions. … Read more
Equal Sets When two sets contains same elements, then they are regarded as equal sets; it’s regardless of the fact in which order these elements are arranged. What matters is that these are identical elements are present in each of the sets. So, here a few examples based on equal sets. Let’s Say: {2, 9, … Read more
When a set is formed with no elements it cannot be termed as nothing but a set with no elements in it. Such sets which contain no elements are addressed as empty set or null set. Empty Set – Definition Defining an empty set would be quite subtle and requires a thought. It is important … Read more
Difference in Set A and Set B or the difference of Set B from Set A, it’s represented by A-B. It’s the set of all elements of set A that in Set B are not present. Mathematically, it is given by: A-B = { x: x∈A and x∉B} If in the condition, (A∩B) refers to … Read more
Relation While you may be seeking a better hand on functions and relations, it may be important to get to explore different elements included within the same. What is a Relation? Relation is said to determine the relationship that prevails between different sets of values. In Mathematics, this relation exists among the values x and … Read more
Suppose we have a set A which is a subset of some Universal Set “U”. The complement of A is a set of elements of the Universal Set, which are not the elements of A. Here, Set A’ complement is estimated w.r.t Universal Set ( Taking everything in mind, Set A refers to a subset … Read more
Parallel to x-axis: All horizontal lines are parallel to the x-axis and they have a slope of 0. When a line is perpendicular to y-axis, it is parallel to the x-axis. In both cases: m = 0 An equation such as y = 2 can be graphed in the coordinate plane. Any pair of values … Read more
A family of lines is a set of lines having one or two factors in common with each other. Straight lines can belong to two types of families: one where the slope is the same and one where the y-intercept is the same. Consider the two straight lines a1x+b1y+c1=0 a2x+b2y+c2=0 For any nonzero constant k, … Read more
The distance between point P= (x0, y0) and Line L: ax +by+c=0 is shown in the figure below. For the general equation L= ax + by +c =0 m = -a/b The shortest distance between a point, P and a line is a perpendicular line segment. The slope of the perpendicular line formed from the … Read more
Cartesian product is determined by the two words that comprise the same. The word Cartesian is said to be derived from the name of a French Philosopher and mathematician René Descartes. The Cartesian product of any two non empty sets say A and B would be denoted and determined as A x B. Also, it … Read more