Notes, summaries, assignments, exams, and problems for Other courses

Multiple Choice Questions

Choose the correct option:

1. Concepts studied under Microeconomics.

   (a) National Income (b) General Price Level (c) Factor Pricing (d) Product Pricing

   Options: (i) a & b (ii) b & c (iii) c & d (iv) only b

   Ans: Option (iii) c & d

2. The law of DMU is important to

   (a) Producer (b) Consumer (c) Government (d) None of the above

   Option: (i) a & b (ii) b & c (iii) d (iv) a, b & c

   Ans: Option (iv) a, b and c

3. When price falls demand

   (a) Rises (b) Contracts (c) Remains constant (d) Becomes Negative

   Option: (i) a (ii) b (iii) c (iv) d

   Ans: Option (i) a

4. Product differentiation is possible in the following market

   a) Perfect competition. b) Monopoly c) Monopolistic competition. d) All of the above

   Option: (1) a &

Pumping Lemma and Non-Regular Languages

9) Define Pumping Lemma. Prove that the language L = { aⁱ b^j | i > j } is not a regular language:

Let L be a regular language. There exists a constant k such that for every string ω in L, where the length of string ω i.e |ω| ≥ k, we can break ω into 3 strings i.e ω = xyz following conditions:

• (i) |xy| ≤ k
• (ii) y ≠ ε i.e |y| > 0
• (iii) for each q ≥ 0, xy^qz ∈ L

Let L be a regular language. w = a^(k+1) b^k is a long string (given k > 0). |w| = 2k + 1, w = xyz should satisfy:

• (i) |xy| ≤ k
• (ii) y ≠ 0
• (iii) for each q ≥ 0, xy^q z ∈ L

Let k = 3, w = a⁴ b³, which is aaaaabbb.

• (i) |xy| ≤ k, 3 ≤ 3
• (ii) y ≠ 0, y = a

Minimization of DFA's

11) Minimization of DFA’s A=(Q, Σ, δ, q₀, F):

Use... Continue reading "Pumping Lemma, Table Filling, DFA Minimization, Parse Trees, Ambiguous Grammars & Context-Free Grammars" »

Unit 1: The Impact of the Internet on Content Production

Jump to Digital

Four decades may seem like a long time, but they represent a complete change in our world.

First ‘80s: first personal computers at home.

During ‘90s: first home connections to the Internet.

During ‘00s: mobile phone spreading.

During ‘10s: smartphone spreading.

The environment of content creation and consumption has changed, as have the habits of creators and consumers.

• From magazines and newspapers to digital media.
• From legacy radio to podcasts.
• From traditional TV to VOD (Netflix, Hulu, HBO...).
• From physical formats to digital for entertainment (subscription-based music, ebooks, online games...).

The digital environment is not just about information; it is also an entertainment... Continue reading "Digital Content Creation: Impact, Architecture, and Monetization" »

Economic Systems of the World

Subsistence System

• Based on the primary sector, families produce what they consume in small quantities. If necessary, they sell or exchange goods on the local market.
• Prevalent before the Industrial Revolution.
• Today, it is only found in less developed societies due to limited access to technology.

Communist System

• The state controls the economy, owning companies and deciding production (what and quantity), prices, distribution of profits, etc.
• Previously common, it is now used in Cuba, Laos, North Korea, Vietnam, and China.
• The Chinese system is a hybrid between communism and capitalism.

Capitalist System

• Means of production are privately owned (technology, companies, machinery, etc.). The motivation to make a profit drives

What People Often Take for Granted

People often take good health, time, and simple moments for granted. We often forget how precious our well-being and the time we spend with family and friends are until we no longer have them.

The Importance of Relationships

My family and close friends play an important role in my life because they provide emotional support, understanding, and help me grow as a person. They’re always there when I need guidance or comfort.

Helping Others: Actions and Impact

I’m willing to listen, offer my help, and volunteer for causes I care about. Sometimes, just being there for someone or donating time and resources can make a big difference in someone’s life.

Social Media's Role in Awareness

Social media can be a powerful... Continue reading "Life's Essentials: Appreciating Moments & Skills" »

Main Goals of Central Banks

Primary Objectives

• Promote steady growth in national output.
• Maintain low unemployment rates.
• Ensure stable and orderly financial markets.

Monetary Policy Actions

Inflation Rising

• Central Bank raises interest rates to reduce price pressures and slow down the economy.

Sluggish Economy

• Central Bank lowers interest rates to boost aggregate demand, output, and reduce unemployment.

Creation of the Federal Reserve System (1907)

• Comprises 12 regional Federal Reserve Banks.
• Key roles include:
  • Conducting monetary policy.
  • Supervising and regulating banks.
  • Ensuring financial stability.
  • Providing financial services to government and public.

Monetary Policy Instruments

Interest Rate

Primary tool for adjusting economic activity.

Open Market Operations

Buying/... Continue reading "Central Bank Functions and Monetary Policy" »

Lenin's Foundation of Soviet Power

Lenin and Stalin were both central figures in Soviet history, shaping the course of the state's political development through authoritarian rule. Lenin, the founder of Soviet Russia, built the foundation for a centralized one-party state, justified by his interpretation of Marxism and the "dictatorship of the proletariat." He exercised political authority through the establishment of key structures like the Soviets, the Cheka (secret police), and the Red Army. Lenin used political repression, such as the Red Terror, to maintain control, and introduced War Communism followed by the New Economic Policy (NEP) to stabilize the economy. Though he centralized power, Lenin maintained a more consultative leadership... Continue reading "Lenin vs Stalin: Soviet Rule Compared" »

 simply supported beam is a structural element supported at both ends, typically resting on supports that allow notation but prevent vertical olisplacement. It is is free to bend under applied loads and is commonly used in bridges and buildings///continuas beam is a structural element that extends over multiple supports, with more than two supports along its length. It distributes loads. Mare evenly, reducing bending moments and deflection compared.//////Overhanging beam An overhanging beam is a beam that extends beyond one or both of its supports, creating a cantilevered section. This type of beam combines characteristics of both simply supported and cantilever beams, experiencing bending moments and shear forced in the overhanging portion.... Continue reading "Understanding Beams, Poisson's Ratio, and Hooke's Law" »