ଦର୍ଶନୀୟତା ଓ ଯୁକ୍ତି (Introduction to Logic)

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Questions and Answers

ହାଇପୋଥେଟିକାଲ୍ ଶିଲୋଗିଜ୍‌ ଦ୍ୱାରା କଣ ସୂଚିତ କରାଯାଇଛି?

ଯଦି p, ତେବେ r (correct)

ଯଦି p, ତେବେ q (correct)

ଯଦି q, ତେବେ p

ଯଦି q ତାହାର ପରେ r

ଡିସଜଙ୍କଟିଭ୍ ସିଲୋଗିଜମ୍ କ'ଣ ତାଲୁକ୍ ରଖେ?

ପୂର୍ଣ୍ଣ କଥା ଅତ୍ୟାଧିକ କରିବା

p ସତ୍ୟ ହେଲେ q

P କିମ୍ବା q (correct)

q ତେବେ r

ଏଠାରେ କୌଣସି ଫ୍ୟାଲେସୀ ନହିଁ, କାହିଁକି?

ଅଡ୍ ହୋମିନେମ୍

ଗତିମାନ କଥା (correct)

ଫାଲ୍ସ ଡିଲେମା

ସ୍ଟ୍ର କାମ୍

ଫର୍ମାଲ୍ ଲୋଜିକ୍ କ'ଣ କୌଣସି ଜିନିଷ ଉପରେ ନିର୍ଭର କରେ?

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ଭୁଲ ମାନିବା ଗୁଣାଙ୍କ ଦେଖାଯାଏ କ'ଣ?

ସ୍ରୋତାଙ୍କର ସମ୍ମାନ Signup and view all the answers

ଲଜିକ୍ କ'ଣ?

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ସାଧାରଣ ବିବେଚନାର ବିଶେଷତା କ'ଣ?

ଏହାକୁ ଛୋଟ ବିବେଚନାରେ ବାଣ୍ଟାଇ ନାହିଁ Signup and view all the answers

କୋଣସି ସଂସ୍ଥାପନା କେବଳ ସତ୍ୟ ସମୟରେ ମିଳିଧାଲା କେଉଁଟା?

ହାଁ Signup and view all the answers

ଯଦି ଏହା ସତ୍ୟ ହୁଏ, ତେବେ ଏହା କେବେ ବୁଝ ନାହିଁ?

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ଧୈର୍ଯ୍ୟର ତାତ୍ତ୍ୱିକ ସୂତ୍ର କ'ଣ?

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ବିଗତ ସମୟରେ ଯାଞ୍ଚ ନହେଲେ କଣସବୁ?

ଲଜିକ୍ ବିକାଶ Signup and view all the answers

ଦ୍ୱାରା ବାଧ୍ୟକରେ ସଠିକ କ'ଣ?

ଏକ ପ୍ରାଧିକାରୀ ସୂତ୍ର Signup and view all the answers

ସମଗ୍ରୀର ସତ୍ୟ ଛୋଟ କ'ଣ?

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Study Notes

Introduction to Logic

Logic is the study of valid reasoning, examining principles of correct inference and argumentation.
Logic distinguishes between sound and unsound arguments.
Logic is crucial in mathematics, philosophy, computer science, and law.

Types of Statements

Statements are declarative sentences, either true or false.
Simple statements cannot be broken down into smaller statements.
Compound statements combine two or more simple statements using logical connectives (e.g., and, or, if...then).
Examples of logical connectives:
- AND: True only if both component statements are true.
- OR: True if at least one component statement is true.
- NOT: Reverses the truth value of the component statement.
- IF...THEN: True unless a true statement leads to a false statement.

Logical Operators

Negation: The opposite truth value of a statement (denoted by ¬ or ~).
Conjunction: "And" (denoted by ∧).
Disjunction: "Or" (denoted by ∨).
Conditional: "If...then" (denoted by →). The "if" part is the hypothesis, the "then" part is the conclusion. A conditional statement is false only when the hypothesis is true and the conclusion is false.
Biconditional: "If and only if" (denoted by ↔). True when both component statements have the same truth value.

Truth Tables

Truth tables determine compound statement truth values for all possible component truth value combinations. They are essential for analyzing argument validity.
A well-constructed truth table produces consistent results matching the logic operators.

Arguments and Validity

Arguments are sets of statements (premises) supporting a conclusion.
Deductive arguments aim to provide conclusive support for the conclusion; if premises are true, the conclusion must be true.
Inductive arguments provide probable support for the conclusion; the conclusion is likely, but not guaranteed, if premises are true.
Validity: In a deductive argument, validity means the conclusion logically follows the premises, regardless of premise truth. A valid argument with true premises is sound.

Types of Deductive Arguments

Modus Ponens: If p, then q. P. Therefore, q.
Modus Tollens: If p, then q. Not q. Therefore, not p.
Hypothetical Syllogism: If p, then q. If q, then r. Therefore, if p, then r.
Disjunctive Syllogism: P or q. Not p. Therefore, q.

Fallacies

Fallacies are errors in reasoning leading to invalid arguments.
Examples of common fallacies:
- Ad hominem: Attacking the person, not the argument.
- Straw man: Misrepresenting an argument to attack it easily.
- Appeal to authority: Claiming something's true because an authority said it.
- False dilemma (either/or fallacy): Presenting only two options when more exist.

Formal Logic

Formal logic uses symbolic representations of arguments.
Quantifiers express how many items in a category meet a condition.
- Universal quantifier (∀): For all.
- Existential quantifier (∃): There exists.

Informal Logic

Informal logic evaluates natural language arguments, identifying strengths and weaknesses without rigid rules.
Critical thinking evaluates and analyzes arguments, separating good reasoning from poor reasoning.

Applications of Logic

Logic is used in mathematics (proofs), computer science (programming), philosophy (evaluating arguments), law (reasoning), and everyday life (assessing arguments, problem-solving).

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ଏହି କ୍ୱିଜ୍ ଦର୍ଶନୀୟତା ଓ ଯୁକ୍ତିର ମୂଳ ନିୟମ ଓ ଭିନ୍ନ ପ୍ରକାରର ବାକ୍ୟଗୁଡିକୁ ଅନୁସନ୍ଧାନ କରିବ। ଏହା ସଠିକ୍ ତଥା ଅସଠିକ୍ କ୍ରମରେ ବିଷୟଗତ ବିଶ୍ଳେଷଣ କରେ, ଯାହା ବିଭିନ୍ନ ବିଭାଗରେ ଦ୍ୱାରା ଗୁରୁତ୍‌ବ ରହୁଥାଏ।