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Basic Set Operations

For two given sets A and B, A∪B (read as A union B) is the set of distinct elements that belong to set A and B or both. The number of elements in A ∪ B is given by n(A∪B) = n(A) + n(B) − n(A∩B), where n(X) is the number of elements in set X.

If a set has “n” elements, then the number of subset of the given set is 2ⁿ and the number of proper subsets of the given subset is given by 2ⁿ-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}.Jan 25, 2020

A set is a well-defined collection of objects, whose elements are fixed and cannot vary. It means set doesn't change from person to person. Like for example, the set of natural numbers up to 7 will remain the same as {1,2,3,4,5,6,7}.

=n(A)+n(B)+n(C)−2n(A∩B)−2n(B∩C)−2. Hint: To solve this type of problem always draw the Venn diagram to simplify the question. From the Venn diagram we will write the statements for each of the sets $A$ ,$B$ and $C$.

Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. ... So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual—as opposed to potential—infinite.Oct 8, 2014

The complement of a set is the set that includes all the elements of the universal set that are not present in the given set.

• Solve by Multiplication Write one equation above the other. Multiply one or both equations until one of the variables of both terms have equal coefficients. Add or subtract the equations. Solve for the remaining term. Plug the term back into the equation to find the value of the first term. Check your answer.

• Use the Following Steps to Solve Word Problems: Identify the problem. Identify what you know. Make a plan. Carryout the plan. Verify that the answer makes sense.

• In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. Variables are also called unknowns and the values of the unknowns that satisfy the equality are called solutions of the equation.