Proof:
We must prove two statements. If x A and x B then, by the statement "two sets A and B are different if there exists an element which belongs to one set but not to the other" and by hypothesis, A = B is contradicted. Thus A B. Similarly B A. If A B, then there is an eleme..
We must prove two statements. If x A and x B then, by the statement "two sets A and B are different if there exists an element which belongs to one set but not to the other" and by hypothesis, A = B is contradicted. Thus A B. Similarly B A. If A B, then there is an eleme..Baye's Theorem
Law of Total Probability: If B 1 , B 2 , B 3 , .., B n are mutually exclusive and exhaustive events of the sample space S, then for any event A of S. Baye's Theorem: Let S be a sample space. If A 1 , A, A 3 ... A n are mutually exclusive and exhaustive events such that P(A i..
Law of Total Probability: If B 1 , B 2 , B 3 , .., B n are mutually exclusive and exhaustive events of the sample space S, then for any event A of S. Baye's Theorem: Let S be a sample space. If A 1 , A, A 3 ... A n are mutually exclusive and exhaustive events such that P(A i..Real Functions and their Graphs
Functions: f is a function from set A to a set B if each element x in A can be associated with a unique element in B. Domain: In the above definition of the function, set A is called domain. Co-Domain: In the above definition of the function, set B is called co-domain. ..
Functions: f is a function from set A to a set B if each element x in A can be associated with a unique element in B. Domain: In the above definition of the function, set A is called domain. Co-Domain: In the above definition of the function, set B is called co-domain. ..Summary
Let A and B be two events. Then, where S is the sample space. Note that simple events of a sample space are always mutually exclusive. Sample space: Set of all possible outcomes of a random experiment. Event : An event of a random experiment is defined as a subset of the sample space. Equ..
Let A and B be two events. Then, where S is the sample space. Note that simple events of a sample space are always mutually exclusive. Sample space: Set of all possible outcomes of a random experiment. Event : An event of a random experiment is defined as a subset of the sample space. Equ..Summary Relations and Functions
>Relation from a set A to a set B is a subset of A x B. - A relation R on a set A is reflexive if a R a, " a A- A relation R on a set A is symmetric if a R b b R a. - A relation R on a set A transitive if a R b and b R c a R c. A relation R is said to be an equivalence relation on A if it..
Relations and Functions-, Types of Functions
>Relation from a set A to a set B is a subset of A x B. - A relation R on a set A is reflexive if a R a, " a A- A relation R on a set A is symmetric if a R b b R a. - A relation R on a set A transitive if a R b and b R c a R c. A relation R is said to be an equivalence relation on A if it..
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