∪: Union of two sets. A complete Venn diagram represents the union of two sets. ∩: Intersection of two sets. The intersection shows what items are shared between categories.

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.

Let’s take a look at some basic formulas for Venn diagrams of two and three elements. n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B) And so on, where n( A) = number of elements in set A.

n(AuB

If A is the set of odd numbers, then the complement of A is the set of even numbers. If B is the set of multiples of 3, then the complement of B is the set of numbers congruent to 1 or 2 modulo 3 (or, in simpler terms, the integers that are not multiples of 3).

In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the “slope-intercept form”.

The difference of set B from set A, denoted by A-B, is the set of all the elements of set A that are not in set B. In mathematical term, A-B = { x: x∈A and x∉B} If (A∩B) is the intersection between two sets A and B then, A-B = A – (A∩B)

A ∩ B is a subset of A and B. Intersection of a set is commutative, i.e., A ∩ B = B ∩ A….Solved examples to find intersection of two given sets:

1. If A = {2, 4, 6, 8, 10} and B = {1, 3, 8, 4, 6}.
2. If X = {a, b, c} and Y = {ф}.

Intersection is an associative operation; that is, for any sets A, B, and C, one has A ∩ (B ∩ C) = (A ∩ B) ∩ C. Intersection is also commutative; for any A and B, one has A ∩ B = B ∩ A. It thus makes sense to talk about intersections of multiple sets.

If A and B are sets, then A ∩ B, read “A intersection B”, is a new set. Its elements are those objects which are in A and in B i.e. those elements which are in both sets. Example If A = {1,2,3,4} and B = {2,4,6,8}, list the elements of the set A ∩ B.

Set the two equations for y equal to each other. Solve for x. This will be the x-coordinate for the point of intersection. Use this x-coordinate and plug it into either of the original equations for the lines and solve for y.

If A and b are two different events then, P(A U B) = P(A) + P(B) – P(A ∩ B). Consider the Venn diagram. P(A U B) is the probability of the sum of all sample points in A U B. Now P(A) + P(B) is the sum of probabilities of sample points in A and in B.

To find the intersection of two straight lines:

1. First we need the equations of the two lines.
2. Then, since at the point of intersection, the two equations will have the same values of x and y, we set the two equations equal to each other.

When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Here, lines P and Q intersect at point O, which is the point of intersection.