Problem checks: SAT ∈ NP because a Boolean assignment is a polynomial-size certificate and we can evaluate the formula in polynomial time.
Reduction (construction):
Given a circuit made only of NAND gates (each gate has two inputs which are either an input wire, a constant T/F, or an earlier gate output), make one Boolean variable for each circuit input and one variable for the output of each gate. For each gate z = NAND(a,b) add CNF clauses that force z to equal ¬(a ∧
💧 WATER CHEMISTRY CHEAT
1. Sources of Water
Source Description Characteristics
Surface Water Rivers, lakes, ponds, reservoirs Contains suspended, colloidal & dissolved impurities
Ground Water Wells, springs, borewells Contains dissolved salts (hardness) but less organic matter
Rain Water Condensed atmospheric water vapour Purest natural form but may contain dissolved gases like CO₂, SO₂
Sea Water Oceanic water Contains ~3.5% salts; not fit for domestic use
2. Impurities in Water
Type...
how nutrients generally move among organisms, origin of mineral N: Atmospheric N₂ is converted into mineral forms (NH₄⁺, NO₃⁻) by: Biological fixation (by bacteria in roots or soil) Lightning fixation Industrial fixation (fertilizers); N cycling: i. Plant uptake and incorporation (mineral → organic N) ii. Resorption before leaf fall (retranslocating nutrients) iii. Decomposition of litterfall (organic → mineral N)
importance of nutrient resorption: Plants withdraw nutrients (like
CHAPTER 4 OVERVIEW – Protein Structure & Function
Proteins are at the center of all biological processes.
They catalyze reactions, regulate pathways, transport molecules, and form most of the structural framework of cells.
Core Principle: Structure → Function.
Key Historical Milestones:
CREATE TABLE Supplier (
SupplierID INT PRIMARY KEY,
Name VARCHAR(100) NOT NULL,
City VARCHAR(50)
);
CREATE TABLE Product (
ProductID INT PRIMARY KEY,
Name VARCHAR(100) NOT NULL,
Price DECIMAL(10, 2) NOT NULL,
SupplierID INT,
FOREIGN KEY (SupplierID) REFERENCES Supplier(SupplierID),
CHECK (Price > 0)
);
INSERT INTO Supplier (SupplierID, Name, City) VALUES
(101, 'Agile Supplies', 'Mumbai'),
(102, 'TechCorp Distributors', 'Delhi'),
(103, 'Global Trading', 'Kolkata'
Paradigms= Interactionism &Critical
Key Principles of Labeling Theory=The focus is on what happens after the action, not what
preceded or caused the action
Primary deviance: occasional or situational behavior that may be
excused or rationalized by the actor or the audience
- The initial act of deviance that goes relatively unpunished
Secondary deviance:deviant behavior triggered by social reactions
that follows primary deviance,deviance that occurs after person is labeled criminal
Conformist=
What are the most common skin conditions needing long term care?
Xerosis (dry skin)
Pruritus (itchy)
What are the Primary Lesions?
1. Macule
2. Patch
3. Papule
4. Plaque
5. Nodule
6. Tumor
7. Wheal
8.Vesicle
9. Bulla
10. Pustule
Define macule
small, ≥1 cm
Define Patch
larger, >1 cm
Define Papule
small, ≤ .5 cm, no visible fluid
Define Plaque
larger, >.5 cm, can be coalescence of papules
Define Nodule
.5-2cm, deeper and firmer than papule
Define Tumor
nodule >2 cm, no fluid
Define Wheal...
*Chapter 1: Nature and Significance of Management*
*Meaning of Management: Process of planning, organizing, staffing, directing, and controlling to achieve organizational goals efficiently and effectively. *Characteristics of Management: Goal-oriented, pervasive, multidimensional (managing work, people, operations), continuous process, group activity, dynamic function, intangible force.
*Functions of Management: Planning, Organizing, Staffing, Directing, Controlling.
*Objectives of Management:
-- Create a new database (optional, good practice)
CREATE DATABASE IF NOT EXISTS StudentDB;
USE StudentDB;
-- ### Create Tables ###
CREATE TABLE Student (
StudentID INT PRIMARY KEY AUTO_INCREMENT,
Name VARCHAR(100) NOT NULL,
Dept VARCHAR(50),
Age INT,
Email VARCHAR(100) UNIQUE NOT NULL,
CHECK (Age > 16)
);
CREATE TABLE Course (
CourseID INT PRIMARY KEY AUTO_INCREMENT,
Title VARCHAR(100) NOT NULL,
Credits INT,
StudentID INT,
FOREIGN KEY (StudentID)