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