Understanding Social Institutions

Institutional Pattern

• An institution has specific goals that benefit society.
• An institution is an abstract concept involving rules, regulations, norms, and values
• These arise through social interaction and regulate the behavior patterns of society members.
• Institutions foster unity among society members.
• They also aid in predicting the behavior of others.
• Certain functions, such as reproduction, are essential for the survival of individuals and groups.
• These functions ensure a continuous supply of society's members.
• They also provide a comforting environment for new members.

Other Functions

• Economic institutions ensure individual self-support.
• Educational institutions educate the young in their society's important teachings.
• Religious institutions control behavior through supernatural phenomena.
• Institutions have numerous folkways, both major and minor.
• Institutions are normative.
• Institutions are independent.

Definitions of Institutions

• According to Mac Iver, an institution is a set of formal procedures that characterize a group, performing a function within society, essentially an organized way of doing something.
• As per Feibelman, an institution is an organized, patterned, traditional way of doing things.
• It includes interwoven folkways, and mores built around one or more functions.
• Douglass North defines institutions as the rules of the game in society, shaping human interaction through constraints.

Key Features of Institutions (Apparent in Definition)

• Institutions are humanly devised, contrasting with other causes like geography.
• They are the rules of the game which sets constraints on human behavior.
• Their influence primarily operates through incentives.

Characteristics of Institutions

• Institutions are a cluster of social usages.
• They have a relative degree of permanence.
• They have well-defined objectives.
• Cultural objects of utilitarian value and symbols characterize them.
• Symbols may be material or non-material.
• Institutions possess established traditions.
• Institutions transmit social heritage.
• Institutions resist social change.
• Institutions both constrain and enable behavior.

Types of Institutions

• According to Sumner, institutions are either crescive (growing) or enacted.
• Crescive institutions, like property, marriage, and religion, originate from mores and are unconscious in their origin.
• Enacted institutions, for example credit and business institutions, are consciously organized for definite purposes.
• According to Ballard, basic institutions are those considered necessary for maintaining a given society, for example family, religious, economic, and educational institutions.

Subsidiary Institutions

• Subsidiary institutions are less essential for maintaining social order.
• Chapin classifies institutions based on their generality or restrictions within society.
• Operative institutions focus on organizing patterns of behavior that facilitate the attainment of objectives.
• Relative institutions are organized to control customs and behavior
• They are not direct parts of the regulative institution itself.

Formal and Informal Institutions

• Formal institutions are openly codified and communicated through widely accepted channels.
• They're products of collective decisions and are imposed exogenously.
• Formal institutions are enforced by a third party, often the state.
• Informal institutions are socially shared rules, often unwritten.
• They are created, communicated, and enforced outside officially sanctioned channels.
• Being generated endogenously, they're unintended outcomes of human action.
• They frequently characterize aspects of traditional culture and personal networks.

Functions of Institutions

• Simplify action for individual society members.
• Provide a means of social change and control.
• Give individuals a role and status.
• Impart order to the society.
• Act as a stimulant.
• They also harmonize agencies in the total cultural environment
• Institutions display tension between stability and change.
• Institutions solve cooperation problems.

Normative Aspect

• This refers to the formal and informal rules, laws, regulations, customs.
• They also refer to traditions that guide and constrain behavior inside institutions.
• These norms offer a framework for understanding individual roles and responsibilities.
• This helps ensure that individual behavior aligns with societal expectations.
• Institutional norms can be explicit or implicit, taking various forms.

Legal Norms

• Institutions often operate within a legal framework.
• This framework defines the rules and regulations that govern behavior.
• It includes laws, regulations, and policies that dictate how individuals should behave.

Social Norms

• Institutions also are shaped by social norms.
• Social norms are unwritten rules and expectations governing behavior within the society and influenced by cultural, religious and historical factors
• These may vary across different institutions and societies.

Sets

• A set is a definite, well-distinguished collection or group.

Set Representation

• Tabular or Roster Form: Lists elements, e.g., ECONOMICS = {E,C,O,N,M,I,S}.
• Rule or Set-Builder Method: Defines a rule.
• For example: B = {x | x is a vowel in the English alphabet}.
• Venn Diagram method

Types of Sets

• Void/Null/Empty Set: Denoted as φ or { }.
• Unit/Singleton Set: Contains only one element, ex: A = {10}.
• Finite Set: Has a countable number of elements.
• Order: Number of elements in that set
• Non-Finite Set: Has an infinite number of elements.
• Universal Set: Contains all possible elements.

Set Relation: Subsets

• If A = {x, y, z} and B = {a, x, y, z}, then A is a subset of B (A ⊆ B).
• Null set is a subset of all sets.
• A set is a subset in itself.
• Number of possible subsets of given set A can be calculated as 2^n where n is the number of elements within that set

Null set

• The null set is the subset of all sets

Subset Example

• For A = {4, 5, 6}, the possible subsets are: {}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}.

Proper Subset

• B is the Proper subset of set A
• No. of Proper subsets = 2^n-1

Power Set

• The power set is the set of all possible subsets of a given set.
• For example: if A = {4, 5, 6}, then P(A) = { {}, {4}, {5}, {6}, {4, 5}, {5, 6}, {4, 6}, {4, 5, 6} }.

Equal Sets

• A = {1, 2, 3} and B = {3, 1, 2} implying A=B.

Equivalent Sets

• If A={1,2,3,4} and B = {a, b, c, d} i.e Disjoined the set . Thus "A is equivalent to B" or "A ↔B".

Comparable

• If one set is a subset of another then we say that these sets are comparable

Operations on Sets

• Union of Sets
  • A ∪ B includes all elements from both A and B.
• Intersection of Sets
  • A ∩ B includes only the elements common to both A and B.
• Difference
• Denoted A-B and only includes the elements found in A and not found in B
• Symmetric Difference
  • A Δ B = (A ∪ B) - (A ∩ B), i.e. elements in either A or B but not in both.

Partition

• The non-overlapping parts in a set
• Every element should be there

Complement of a Set

• The complement of set A ( A^c ), includes all elements that are not in A but in the universal set U.

Cartesian Product of Two Sets

• Denoted A x B and this relates to a set of ordered pair

Useful equations

• Order of (A x B) = Order of (A) x Order of (B)
• n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
• If disjoint set n(A ∪ B) = n(A) + n(B)
• n(A ∪ B ∪ C)= n(A) + n(B)+ n(C)- n(A∩B)- n(B∩C) - n (C∩A)+ n(A∩B∩C)

Chapter 2: Relations and Functions

• A relation, denoted as R, is a subset of A x B.

Domain of a Relation

• The domain of a relation is the set of all the first elements which belong to the ordered pairs.

Range of Relations

• It relates to ordered pain

Functions

• This Includes the association of each element

Reflection

• Single Valved Function

Limit

• A limit can only be evaluated if x approaches a, where f(x) = L
• The limit of f(x) = x + 4 when x approaches to 2 is 6
• Limit f(x) = 6 when x→2
• f(x) = (x^2-4)/(x-2)
• At x=2, limit cannot exist

Methods of substitution

• Substitute terms into a existing function to generate the limit
• Rationalise and then substitute to find the limit

Formulae

• d/dx (uv)
  • u dv/dx + v du/dx
• d/dx (uvw)
  • uv dw/dx + uw dv/dx + vw du/dx
• y = u/v
  • dy/dx = (v du/dx - u dv/dx) / v^2
• du^n/dx = nu^n-1 du/dx
• Power rule
  • d(x^n)/dx = n x^n-1
• dy/dx = dy/du du/dx
• d/dx (log a x) = 1/(x log a )
• d/dx e^x = e^xx log a

Maxima and Minima Conditions for finding Maxima / Minima for function

• Step 1 - y= x^3-12 x generate
  • dy/dx = 3x^2-12=0 and solve
• A = x + 1 , Maximum Value is less than minimum value
• y = log x/x, find the maxima value

Terminologies

• 30 - 10 and therefore it is more efficient compared to 2.

General Knowledge and current affairs

• Indian Knowledge System in second semester in all higher education institutions

Matrices

• It includes row and column
• Matrix m x n and the number of elements will be related to row and column

Types of Matrices

• Row Matrix
• Column Matrix
• As all elements are not corresponding
• Square Matrix: rows = column .
• Diagonal Matrix
• Scalar / Unit Matrix
• Zero Matrix
• Upper and Lower Triangular Matrices
• Traspose Matrix = If A^T = A then Symmetrix matrix , If A^T = -A then Skew symmetrix matrix.

Useful calculations

• A x B then simply proceed as usual
• In order too mutiply you follow -8,
• If it is multiplied with A-B then 4 -2 x2 + = = 4+2 = A

3 individual Ram, Shyam and Sunder want for the market so if we calculate bill

• Ram = Bill
• Shyam = Bill
• Sunder = Bill

Determinants of a Matrix

• In the event A = ( 13/ 24)
• then it is expressed as |𝐴| = 1 𝑥 4 − 3 × 2 -2
• Crammer's Rule
• To find the value for D

Rank of a Matrix

• rank(A) ≤ min(number of rows, number of columns).
• If all the Matrixs equal to its is determinant then its shows that the rank of the Matrix will have some 3 - digit number

Skewness

• Direction of Variation/ Diff b/w central term
• Kaul Pearson's Method
  • Skewness = Mean - Mode
• Coefficient of skewness = Mean-Mode devided by Standard Deviation
• Mode = 3 Median to the power of 2 x Mean
• Yule's method Skewness a3 + a1 - 2 Median Quartie
• Coefficient of skewness = a.3 + a1 - 2Median - divide by number by a1 - divide number be 1. Kelly's Method Percentile
• Skewness = Pool + Tool-2Median Or
  • Coefficient of skewness Pool + Tool + 2 Median pool toll