7th pay commission news | 40,000₹ pay hike for these Central Government employees

2019 is going to be a great year as this year Lok Sabha elections are going to be held and to attract the voters, PM Modi government is trying all possible ways. The long pending issues of 7th pay commission which were held by Modi government or seems to be that they were kept on hold intentionally for the year 2019, so that they can clear the issues and can attract the Central Government employees and many more sectors of public.
from the first day of the January 2019 it is being notices that Modi government is clearing the 7th pay commission issues of many departments one by one. Earlier it has cleared the 7th pay commission issue of railway staffs. Now it is decided to clear 7th pay commission issue of this department with a great hike in salary upto 40000 rupees per month.

Viewing 2019 Lok Sabha election, Modi government has announced Hugh pay hike for lecturers and professors in every state.
These academic staffs will get the benefits of the 7th Pay Commission with effect from January 1, 2016. The central government has said that with the teachers, other staff of universities and colleges will also get a new pay scale.
Houses easy steps will get user arears.

Lucknow University Associated College Teachers Association (LUACTA) president Manoj Pandey told to a news platform zeebiz.com that implementation of the 7th pay commission will increase the salaries by about Rs 40,000 at professor level while those at the lower level will get a hike up to Rs 7,000. 

Manoj Pandey said that the University Grant Commission (UGC) had issued a notice on November 2 to increase the salary of university teachers and employees. However, several states had not implemented the order. Now, after the central government's decision, it will be implemented across the country.

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अब ऑफिस के बाद बॉस का फोन उठाना जरूरी नहीं, नौकरीपेशा लोगों के लिए खुशखबरी

अब ऑफिस के बाद बॉस का फोन उठाना जरूरी नहीं, नौकरीपेशा लोगों के लिए खुशखबरी

Thursday, 10 Jan, 11.11 am

Sources: oneindia.com

नई दिल्ली। देशभर में नौकरीपेशा लोगों को ऑफिस के बाद भी फोन पर व्यस्त देखा जाता है। इसके अलावा कभी घर बैठकर वे ईमेल भी करते रहते हैं। इससे सिर्फ उनकी निजी जिंदगी पर प्रभाव पड़ता है बल्कि उनके परिवार को भी उनका पूरा समय नहीं मिल पाता। ऐसे में लोकसभा में एनसीपी की सांसद सुप्रिया सुले ने एक प्राइवेट मेंबर बिल पेश किया है।

इस बिल के बारे में जानकर सभी नौकरीपेशा लोग खुश हो जाएंगे। दरअसल इस बिल के अनुसार अगर एक बार आपके नौकरी ऑवर्स पूरे हो जाते हैं तो आपको पूरा अधिकार है कि आप ऑफिस के किसी कॉल या ईमेल का जवाब न दें।

राइट टू डिस्कनैक्ट नाम से ये बिल इसलिए लाया जा रहा है ताकि कर्मचारियों के स्ट्रेस को कम किया जा सके।

जिससे कि कर्मचारी की दफ्तरी और निजी जीवन के बीच का तनाव खत्म हो जाएगा। बता दें कि न सिर्फ भारत में बल्कि कई अन्य देशों में भी इस तरह के बिल को लेकर चर्चा चल रही है। फ्रांस, न्यूयार्क और जर्मनी में इसे पेश किया गया। ये विधेयक 28 दिसंबर को पेश किया गया और इसमें कहा गया कि एक कर्मचारी कल्याण प्राधिकरण की स्थापना की जाएगी. इस प्राधिकरण के भीतर आईटी, लेबर मंत्री और कम्यूनिकेशन शामिल होंगे।

RELATIONS AND FUNCTIONS : MATHEMATICS XII CLASS

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Types of Relations
In this section, we would like to study different types of relations. We know that a relation in a set A is a subset of A × A. Thus, the empty set ⍷ and A × A are two extreme relations.


For illustration, consider a relation R in the set A = {1, 2, 3, 4} given by R = {(a, b): a – b = 10}. This is the empty set, as no pair (a, b) satisfies the condition a – b = 10. Similarly, R' = {(a, b) : | a – b | >= 0} is the whole set A × A, as all pairs (a, b) in A × A satisfy | a – b | >= 0. These two extreme examples lead us to the following definitions.

Definition 1 A relation R in a set A is called empty relation, if no element of A is related to any element of A, i.e., R = ⍷ A × A.


Definition 2 A relation R in a set A is called universal relation, if each element of A is related to every element of A, i.e., R = A × A.

Both the empty relation and the universal relation are some times called trivial relations.

Example 1 Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R' = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Solution Since the school is boys school, no student of the school can be sister of any student of the school. Hence, R = ⍷, showing that R is the empty relation. It is also obvious that the difference between heights of any two students of the school has to be
less than 3 meters. This shows that R' = A × A is the universal relation.



Remark In Class XI, we have seen two ways of representing a relation, namely
roaster method and set builder method. However, a relation R in the set {1, 2, 3, 4}
defined by R = {(a, b) : b = a + 1} is also expressed as a R b if and only if
b = a + 1 by many authors. We may also use this notation, as and when convenient.
If (a, b) ⍷ R, we say that a is related to b and we denote it as a R b.
One of the most important relation, which plays a significant role in Mathematics,
is an equivalence relation. To study equivalence relation, we first consider three
types of relations, namely reflexive, symmetric and transitive.


Definition 3 A relation R in a set A is called
(i) reflexive, if (a, a) ⍷ R, for every a ⍷ A,
(ii) symmetric, if (a1, a2) ⍷ R implies that (a2, a1) ⍷ R, for all a1, a2 ⍷ A.
(iii) transitive, if (a1, a2) ⍷ R and (a2, a3) ⍷ R implies that (a1, a3) ⍷ R, for all a1, a2✱
a 3 ⍷  A.
Definition 4 A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive.

Example 2 Let T be the set of all triangles in a plane with R a relation in T given by R = {(T1, T2) : T1 is congruent to T2}. Show that R is an equivalence relation.


Solution R is reflexive, since every triangle is congruent to itself. Further, (T1, T2) ⍷ R =>T1 is congruent to T2 => T2 is congruent to T1 => (T2, T1) ⍷ R. Hence, R is symmetric. Moreover, (T1, T2), (T2, T3) ⍷ R => T1 is congruent to T2 and T2 is congruent to T3 => T1 is congruent to T3 => (T1, T3) ⍷ R. Therefore, R is an equivalence relation.

Example 3 Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive.

Solution R is not reflexive, as a line L1 can not be perpendicular to itself, i.e., (L1, L1) => R. R is symmetric as (L1, L2) ⍷ R✞ L1 is perpendicular to L2 =>L2 is perpendicular to L1=> (L2, L1) ⍷ R. R is not transitive. Indeed, if L1 is perpendicular to L2 and L2 is perpendicular to L3, then L1 can never be perpendicular to L3. In fact, L1 is parallel to L3, i.e., (L1, L2) ⍷ R, (L2, L3) ⍷ R but (L1, L3) => R.

Example 4 Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

Solution R is reflexive, since (1, 1), (2, 2) and (3, 3) lie in R. Also, R is not symmetric, as (1, 2) ⍷ R but (2, 1) => R. Similarly, R is not transitive, as (1, 2) ⍷ R and (2, 3) ⍷ R but (1, 3) => R.

Example 5 Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} is an equivalence relation.

Solution R is reflexive, as 2 divides (a – a) for all a ⍷ Z. Further, if (a, b) ⍷ R, then2 divides a – b. Therefore, 2 divides b – a. Hence, (b, a) ⍷ R, which shows that R is symmetric. Similarly, if (a, b) ⍷ R and (b, c) ⍷ R, then a – b and b – c are divisible by
2. Now, a – c = (a – b) + (b – c) is even (Why?). So, (a – c) is divisible by 2. This
shows that R is transitive. Thus, R is an equivalence relation in Z.