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Introduction to Logic

1. Number Series


A sequence of numbers arranged in a specific pattern or rule.
Common tasks include identifying the next number in the series or finding a missing number.
Patterns may involve addition, subtraction, multiplication, division, or other mathematical relationships.

2. Coding-Decoding

A type of logical reasoning where a word, number, or phrase is coded in a particular way and needs to be decoded based on the given pattern.

Example:
Coding: CAT = DBU (each letter is shifted one position forward).
Decoding: DOG = ?

3. Odd Man Out Series

Identifying the element that does not follow the same pattern or rule as the others in a given series.
Requires analyzing all options and spotting the anomaly.

4. Direction Sense Test

Evaluates an individual's ability to track directions (North, South, East, West) based on given instructions.
Involves concepts like left/right turns, distances traveled, and final positions relative to a starting point.

5. Seating Arrangements

Involves arranging people or objects according to specific rules or clues.
Linear Arrangement: A straight-line arrangement, where participants may face a specific direction.
Circular Arrangement: Participants are arranged in a circle, facing inward or outward.

6. Blood Relations

Logic-based problems involving family relationships.
Requires understanding terms like mother, father, sibling, cousin, etc., and deducing relationships based on given clues.

7. Arithmetic and Geometric Progressions

Arithmetic Progression (AP): A sequence in which each term is obtained by adding a fixed constant to the previous term.
Formula for 𝑛th term: 
𝑎𝑛=𝑎+(𝑛−1)𝑑, where 𝑎 is the first term and 𝑑 is the common difference.

Geometric Progression (GP): A sequence in which each term is obtained by multiplying the previous term by a fixed constant.
Formula for 𝑛th term: 
𝑎𝑛=𝑎⋅𝑟𝑛−1, where 𝑎 is the first term and 𝑟 is the common ratio.

8. Inductive and Deductive Reasoning

Inductive Reasoning: Deriving general conclusions based on specific observations or examples. It is probabilistic and often used for hypothesis formation.
Example: Observing that "all swans seen so far are white" and concluding "all swans are white."

Deductive Reasoning: Drawing specific conclusions based on general rules or premises. It guarantees the correctness of conclusions if premises are true.
Example: All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.

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