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The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S). If a set S is finite, say S has n elements, then the power set of S can be shown to have 2 n elemen..

The countable numbers are called Natural Numbers. Therefore 1 is the smallest or least of all natural numbers. The highest natural number cannot be said because Natural numbers are infinite. The set of Natural numbers is a subset of Rational number..

An ordered pair has a pair of elements which occur in a definite order. Cartesian Product - Given two sets A and B, all possible ordered pairs (x, y) obtained such that x A and y B is called the cartesian product of the sets A and B and is denoted by A x B. Relation - If A an..

Special Parallelograms - Rectangles, rhombuses and squares belong to the set of parallelograms. Each of these may be defined as a parallelogram as follows: A rectangle is an equiangular parallelogram. A rhombus is an equilateral parallelogram. A square is an equilateral and equiangular parallelogra..

Relations - A relation R is a non-empty sub-set of a cartesian product. A relation R is a non-empty sub-set of a cartesian product. A relation is a set of ordered pairs, i.e., R A x B where A and B are two non-empty sets. If R is a relation, write x R y or (x, y) R and we say x ..

An ordered pair has a pair of elements which occur in a definite order. An ordered pair has a pair of elements which occur in a definite order. Cartesian Product - Given two sets A and B, all possible ordered pairs (x, y) obtained such that x A and y B is called the cartesian product of th..

Question: Let A = {1, 2, 3}, B = {2, 3, 4, 5} and C = {3, 4, 5, 6} be three subsets of the universal set U = {1, 2, 3, 4, 5, 6, 7}. Verify the following identities Answer: ..

1. Sample space: Set of all possible outcomes of a random experiment. 2. Event : An event of a random experiment is defined as a subset of the sample space. 3. Exhaustive outcomes: All the outcomes of a random experiment. 4. Random variable: A real valued function ..

A well-defined collection of definite objects is called a set. In roster method of representing a set, all the elements are listed in the set. In property method of representing a set, all the elements are represented by stating all the properties which are satisfied by the elements of the ..

(1) " January has 31 days” is a statement. (2) "Null set is a subset of every set” is a statement. (3) "All girls are studious” is not a statement. (4) "Apoorva is honest” is not a statement. Some sentences depend on a variable for its trut..