Class 11 Applied Mathematics Chapter 7 Mathematical and Logical Reasoning NCERT Book PDF gives students the official chapter text for statements, negation, compound statements, quantifiers and reasoning-based questions. The PDF follows the 2026-27 NCERT chapter and is useful for school tests, CUET-style aptitude practice and quick concept revision.
- Official source: download the original NCERT chapter PDF with printed examples and exercises.
- Best for practice: use it before solving questions on truth values, implications and syllogism.
- 2026-27 ready: the chapter supports the Class 11 Applied Mathematics reasoning unit.
This chapter PDF is the reference text students should keep open while revising statement logic, truth tables and aptitude-style reasoning questions.
Student Feedback: In a Collegedunia poll of more than 10,000 students before the 2026 boards, students said Mathematical and Logical Reasoning became easier when they wrote every condition as a clear statement first. The most common mistake was reversing an if-then statement without checking its converse.
Mathematical and Logical Reasoning NCERT Book PDF for Class 11 Applied Mathematics
The NCERT Book PDF is the base text for this reasoning chapter. It explains how a sentence becomes a mathematical statement, how to form its negation, and how to test whether a conclusion follows from given conditions.
| Chapter part | What students read in the PDF | Why it matters |
|---|---|---|
| Statements | Sentences that can be judged true or false | Builds the base for truth-value questions |
| Logical connectives | And, or, if-then and if and only if forms | Helps students combine simple statements |
| Negation | How to write the opposite of a statement correctly | Prevents mistakes in quantified sentences |
| Reasoning questions | Syllogism, coding-decoding and relation-based tasks | Connects chapter theory to aptitude practice |
Statements, Truth Values and Negation in the NCERT Chapter
The chapter starts with the idea of a statement. A mathematical statement must have a definite truth value. Questions such as opinions, wishes and commands are not statements because they cannot be marked true or false in the same way.
- Statement test: ask whether the sentence is definitely true or false.
- Negation rule: write the exact opposite without changing the topic.
- Quantifier care: the negation of all is at least one not.
- Example habit: test a statement with one simple example before generalising.
A correct negation changes the truth value but keeps the original meaning under check.
Compound Statements and Logical Connectives in Class 11
Compound statements join two or more simple statements. The NCERT PDF uses connectives such as and, or, if-then and if and only if. Students should read these words carefully because each one changes the truth condition.
| Connective | Meaning in the chapter | Fast check |
|---|---|---|
| p and q | Both statements must be true | One false part makes it false |
| p or q | At least one statement is true | Both false makes it false |
| If p then q | p is the condition and q is the result | Do not reverse it blindly |
| p if and only if q | Both directions are being claimed | Check p to q and q to p |
Mathematical and Logical Reasoning Quick Revision
Source: Magnet Brains on YouTube
Implication, Converse, Inverse and Contrapositive in the Book PDF
Implication is the section where many students lose marks. The statement if p then q has three related forms. The converse is if q then p. The inverse is if not p then not q. The contrapositive is if not q then not p.
- Original statement: if p then q.
- Converse: reverse the order, so it becomes if q then p.
- Inverse: negate both parts without reversing them.
- Contrapositive: reverse and negate both parts.
The contrapositive has the same truth value as the original implication. The converse and inverse must be checked separately.
Mathematical Reasoning vs Logical Reasoning Decision Table
Mathematical reasoning focuses on statements and proof-like language. Logical reasoning applies the same clarity to patterns, relations and conclusions. The NCERT chapter helps students move between both forms without treating reasoning as guesswork.
| Question type | Likely skill | What to check first |
|---|---|---|
| Negate a statement | Mathematical reasoning | Exact opposite meaning |
| Find a valid conclusion | Logical reasoning | Given facts only |
| Check if an implication is true | Mathematical reasoning | Condition and result |
| Solve coding or relation clues | Logical reasoning | Pattern, order and relation |
How to Use the Class 11 Applied Mathematics NCERT Book PDF
The PDF works best when students read the definitions first and then solve the exercise questions slowly. Reasoning chapters reward careful wording more than speed in the first attempt.
| Study pass | What to do | Target |
|---|---|---|
| Pass 1 | Read definitions of statement, negation and implication | Understand the language |
| Pass 2 | Make a small truth-condition table for each connective | Avoid formula-like guessing |
| Pass 3 | Solve exercise questions and compare with notes or solutions | Improve accuracy in reasoning steps |
Related Class 11 Applied Mathematics Resources for Mathematical and Logical Reasoning
Also Check: use the original book PDF with the matching notes, solutions and handwritten notes for the same chapter.
| Resource | Best used for | Link |
|---|---|---|
| NCERT Notes | Fast recall of statements, negation and reasoning rules | Mathematical and Logical Reasoning Class 11 Notes |
| NCERT Solutions | Step-by-step answers to textbook questions | Mathematical and Logical Reasoning Class 11 NCERT Solutions |
| Handwritten Notes | Quick visual recall before practice | Mathematical and Logical Reasoning Class 11 Handwritten Notes |
Class 11 Applied Mathematics NCERT Book PDFs for All Chapters
Related Links: download neighbouring NCERT Book PDFs in the same Applied Mathematics format.
| Chapter | Class 11 Applied Mathematics NCERT Book PDF |
|---|---|
| Chapter 3 | Set Class 11 NCERT Book PDF |
| Chapter 4 | Relations Class 11 NCERT Book PDF |
| Chapter 5 | Sequences and Series Class 11 NCERT Book PDF |
| Chapter 6 | Permutations and Combinations Class 11 NCERT Book PDF |
| Chapter 8 | Calculus Class 11 NCERT Book PDF |
| Chapter 9 | Probability Class 11 NCERT Book PDF |
Mathematical and Logical Reasoning Class 11 Applied Mathematics NCERT Book PDF FAQs
Ques. What does the Mathematical and Logical Reasoning NCERT Book PDF contain?
Ans. It contains the official NCERT chapter text, examples and exercises on statements, negation, logical connectives, implication and reasoning questions.
Ques. Is this Class 11 Applied Mathematics Chapter 7 PDF useful for 2026-27 exams?
Ans. Yes. The PDF supports the 2026-27 Applied Mathematics reasoning unit and helps students practise statement logic and aptitude-style reasoning.
Ques. What is the difference between converse and contrapositive?
Ans. Converse reverses the parts of an implication. Contrapositive reverses and negates both parts, and it has the same truth value as the original implication.
Ques. How should students use this NCERT Book PDF?
Ans. Read each definition first, write small examples for connectives, then solve the exercise questions using notes and solutions for checking.
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