Unix Commands Files and Directories These commands allow you to create directories and handle files. Given below is the list of commands in Files and …

Read More »## Unix Architecture

Unix Architecture Here is a basic block diagram of a Unix system − The main concept that unites all the versions of Unix is the following four basics − Kernel − The kernel is the heart of the operating system. It interacts with the hardware and most of the tasks …

Read More »## Unix operating system

Unix Operating System The Unix operating system is a set of programs that act as a link between the computer and the user. The computer programs that allocate the system resources and coordinate all the details of the computer’s internals is called the operating system or the kernel. Users communicate …

Read More »## Probability ugc net exam

Probability Formula Probability is based on observations of certain events. Probability of an event is the ratio of the number of observations of the event to the total numbers of the observations. An experiment is a situation involving chance or probability that leads to results called outcomes. An outcome is the …

Read More »## Equivalence and Partial Orderings

Equivalence relations Definition: A relation R is an equivalence relation if and only if it is reflexive, symmetric and transitive. Examples: Let m and n be integers and let d be a positive integer. The notation m º n (mod d)is read “m is congruent to n modulo d“. The …

Read More »## The Inclusion-Exclusion Principle

The Inclusion-Exclusion Principle (for two events) For two events A, B in a probability space: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Don’t use this to “prove” Kolmogorov’s Axioms!!! Proof: P(A ∪ B) = P(A ∪ (B \ A)) (set theory) The Inclusion-Exclusion Principle (for two …

Read More »## sets relation and function of ugc net exam

## Set Theory Tutorial | Problems, Formulas, Examples

Set theory has its own notations and symbols that can seem unusual for many. In this tutorial, we look at some solved examples to understand how set theory works and the kind of problems it can be used to solve. Definition “A set is a collection of objects.” It is …

Read More »## Pigeonhole Principle for ugc net exam

Pigeonhole Principle Theorems If k+1 or more objects are put in k boxes, then at least one box contains two or more objects. If n objects are put in k boxes, then at least one box contains dn=ke objects. Example: 1) 42 birds share …

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