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  🧩 1. Propositions 🔍 Definition: A proposition is a statement that is either true or false , but not both. 🐄 Animal Science Example : "The cow is ruminant." → ✅ Proposition (It can be verified as true or false) 💹 Economics Example : "Increasing taxes always decreases consumer spending." → ✅ Proposition (It has a truth value, though we may debate its accuracy) ads 🚫 Not Propositions: Questions: “Is the cow healthy?” Commands: “Increase the price!” These cannot be judged as true or false, so they are not propositions. 🔗 2. Arguments (Valid and Invalid) 🔍 Definition: An argument is a series of propositions where: One or more are premises (assumed to be true) One is a conclusion The goal : check whether the conclusion logically follows from the premises. ads ✅ Valid Argument If the conclusion logically follows from the premises. Example (Animal Science): Premise 1: All poultry need clean water. Premise 2: These...

  🧠 What is Reasoning? Reasoning is the mental process of drawing conclusions from facts, observations, or assumptions. In both animal science and economics, the way we reason determines how we: Analyze problems Test hypotheses Interpret data Make decisions add There are three primary types of reasoning approaches: Deductive reasoning Inductive reasoning Abductive reasoning 1️⃣ Deductive Reasoning: From General to Specific 🔍 Definition: Deductive reasoning starts with a general principle or theory and applies it to a specific case to reach a logically certain conclusion. add ✔️ Structure: If A is true , and B fits A , then B must be true . 🐄 Animal Science Example : Premise 1: All ruminants have a four-chambered stomach. Premise 2: Cows are ruminants. ➡️ Conclusion: Cows have a four-chambered stomach. 💹 Economics Example : Premise 1: When demand increases and supply remains constant, prices rise. Premise 2: Demand for wh...

🧠 What Is Logic? Logic is the science of correct reasoning. It teaches us how to think clearly , reason systematically , and draw reliable conclusions based on evidence. It's not just about solving philosophical puzzles — logic is deeply practical . Whether you're studying animal behaviour or economic patterns , logic helps you separate fact from opinion , evidence from assumption , and truth from confusion . 📌 Simple definition : Logic is a tool that helps us think right , argue better , and make smarter decisions .   🌿 Why Logic Matters in Animal Science Animal science is all about observation, interpretation, and decision-making — all of which depend on sound reasoning. 🔍 Real-Life Relevance: Research design : Logic helps you set up experiments with clear, testable hypotheses. Example : If you observe changes in feeding behaviour, is it due to a new diet or environmental stress? Logic helps structure that analysis. Data interpretation : When analysing pattern...

  🧩 1. Introduction Understanding how variables are related is key in zoology and ecology. These relationships help scientists: Analyze biological and ecological data. Make predictions. Understand cause-effect patterns in nature. Variables can be represented using: Tables Graphs Mathematical functions 🔄 2. Types of Relationships Between Variables 🔹 Direct (Positive) Relationship Definition : When one variable increases, the other also increases. Example : As temperature increases , metabolic rate in reptiles increases. Graph : Upward-sloping line or curve. 🔹 Inverse (Negative) Relationship Definition : When one variable increases, the other decreases. Example : As population density increases, resource availability decreases. Graph : Downward-sloping curve. 🔹 No Relationship (Independent Variables) Definition : Change in one variable does not affect the other. Example : No relationship between shoe size and income . ...

🧠 1. Introduction to Probability   🔹 What is Probability?  Probability is a way of measuring how likely an event is to happen. It's used when there is uncertainty about the outcome.   🔹 Probability Space A probability space includes:   Sample space (Ω): All possible outcomes of an experiment. E.g., Ω = {infected, not infected} for testing a cow for a disease.   Event space (𝓕): Collection of events we are interested in. E.g., event E = {infected}.    Probability (P): A number between 0 and 1 assigned to each event.  E.g., P(E) = 0.3 means a 30% chance of infection.   🧪 Example: Let’s say in a herd of 100 animals, 25 have a parasitic infection. P(infection) = 25/100 = 0.25   🔄 2. Conditional Probability  🔹 What is it?  Conditional probability is the chance of one event happening given that another has already occurred.    📌 Formula: 𝑃 ( 𝐴 ∣ 𝐵 ) = 𝑃 ( 𝐴 ∩ 𝐵 ) 𝑃 ( 𝐵 ) P(A∣B...

  I. Introduction to Confidence Intervals: A confidence interval is a range of values that is likely to include the true parameter of interest. In the context of estimating the mean, it provides a range within which we are reasonably confident the true population mean lies. Confidence intervals are useful because they convey both point estimates and a measure of uncertainty. II. Basics of Confidence Intervals for the Mean: Formula for Confidence Interval: � ˉ ± � ( � � ) x ˉ ± t ( n ​ s ​ ) � ˉ x ˉ is the sample mean. � t is the critical t-value from the t-distribution. � s is the sample standard deviation. � n is the sample size. III. The t-Distribution: The t-distribution is used when the sample size is small or when the population standard deviation is unknown. It is similar to the normal distribution but has fatter tails, accommodating the additional uncertainty associated with small sample sizes. IV. Calculating the Critical t-Value: The critical t-value is determined by...