Among the different types of sets, finite and infinite sets are the two that are generally considered while dealing with mathematics. As per those it could be considered as a way to group similar objects. Sets Any considerable collection of mathematical objects that is well-defined can form a set. These objects could probably be anything … Read more
Among the different types of sets, finite and infinite sets are the two that are generally considered while dealing with mathematics. Both of them are self-explanatory with their names; while ‘finite’ explains it to be countable and ‘infinite’ means uncountable. As we get deeper into this discussion, you would be able to understand things much … Read more
De Morgan’s Law refers to the statement that the complement belonging to union of two Sets, Set A and Set B is equal to an intersection of two sets i.e. Set and Set B’s complement. As per De Morgan’s law, also, the intersection of two sets, Set A and Set B’s complement is equal to … Read more
When the graph of a linear function passes through the points A (x1, y1) and B (x2, y2), then the equation can be written as: $y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})$ It can also be written as: $\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}$ For verifying this equation let P(x,y) be any point on the given line that passes through A(x$_{1}$,y$_{1}$) and B(x$_{2}$,y$_{2}$), as shown in … Read more
The slant or slope between any two points on a straight line is always equal. A line on the Cartesian plane can be described by a linear equation. If and two points exist on a line then the slope of the line can be written as: A line has a +ve slope if it is … Read more
Union and intersection are some of the most common operations performed with sets. In mathematics, operations like addition, multiplication, subtraction etc are commonly performed. These operations tend to take one or more operand and give away the results based on the performed operation. Similarly, in the set theory, several operations are performed for two or … Read more
See the word problems solved here to get the basic ideas on how you should be using properties of set’s union and intersection. Word Problems: Example 1. Let finite sets, Set A and Set B like n (A) = 25, n (B) = 29; n (A ∪ B) = 38, so, find – n (A … Read more
Ordered pairs are considered to be a fundamental part as far as graphing is considered. Ordered pairs are important to plot various functions on the graph and ordered functions when plotted on graph will determine how the function looks like on the graph. What is an ordered pair? An ordered is determined as a set … Read more
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