# RS Aggarwal Class 11 Chapter 29 Solutions (Mathematical Reasoning)

In RS Aggarwal Class 11 Solutions for Chapter 29, we will use logic to find out the answers for the basic mathematical reasoning. This Chapter is easy but tricks most of the students therefore RS Aggarwal Class 11 Solutions for Chapter 14 provides students with the easy methods of solving these questions. We have used several logics to solve the questions of this Chapter and hence you can solve any question related to the Chapter if you refer to our RS Aggarwal Class 11 Solutions.

This chapter consists of 4 exercises which have 17 questions in total which have further some parts in them. RS Aggarwal Solutions provides us with rules for determining the validity of the given argument for proving the theorem. Clear explanations of all the 12 questions are provided along with the easy ways to solve the questions.

Instasolv works as a perfect platform for your studies and exam preparation. At Instasolv, our team of subject matter experts frame the Solutions in a way which makes it easy for you to learn and remember the concepts. RS Aggarwal Class 11 Maths Solutions for Chapter 29 are a must to have while preparing any topic of the Chapter, whether it is exam preparation or for competitive exam preparation.

## Important Points of Chapter 29 – Mathematical Reasoning

- There are 2 kinds of reasoning in mathematical language: Deductive logic and Inductive logic.
- Logic is something which deals with the method of reasoning.
- The mathematical statement is the basic unit involved in mathematical reasoning.
- Every true statement is not a valid statement.
- Statements are denoted by small letters i.e. a, b,c etc.
- Mathematical induction is a sort of inductive reasoning.
- An open statement with a Quantifier becomes a Statement and is called a quantified statement.
- The number of rows of the table depends on the number of statements.
- If a is false, then ~ a is true.
- If A is true, then ~ aa is false.
- The converse of a => b is b => a.
- The inverse of a => b is ~ a => ~ b.
- The contrapositive of a => b is ~ b => ~ a.
- A statement which is neither a tautology nor a contradiction is a contingency.

### Topics Covered Under Chapter 29: Mathematical Reasoning

- Deductive reasoning
- Declarative sentences
- Imperative sentences
- Interrogative sentences
- Exclamatory sentences
- Logic
- Statement
- An open and compound statement
- Truth value
- Truth table
- The truth table for 2 statements
- Basic logic connections table
- Contradictions
- Quantifiers and quantified statements
- Laws of the algebra of statements
- Elementary operations of logic

- Conjunction
- Disjunction
- Negation
- Conditional Sentence
- Biconditional Sentence

### How to find out the Validity of Statements for Solving Questions

A statement is said to be valid or invalid according to the situation if it’s true or false.

If a and b are 2 mathematical statements, then the statement

- “ a and b” is true if both a and b stand to be true
- “ a or b “ is true if a is false

b is true or b is false —> a is true

- “If a, then b” is truly a is true —> b is true

Or

b is false

—> a is false

Or a is true and b is false less us to a contradiction

- “ a if and only if b” is true, if

- a is true —> b is true and
- b is true —> a is true

### Exercise Wise Discussion of RS Aggarwal Class 11 Chapter 29

**Exercise 29 A**

This exercise 29A has 3 questions in which you have to:

- Find the statements from the given sentences, and state the statement as true or false
- Answer the following statements is true or false and justify the reason

**Exercise 29 B**

This exercise 29B has 4 questions in which you have to:

- Split given sentences into simple sentences and state whether it’s true or false
- Determine whether inclusive or exclusive is used in the statement
- Find the truth set from the given set on n of open sentences
- Determine the statements as true or false when a set is given

**Exercise 29 C**

This exercise 29C has 5 questions in which you have to:

- Rewrite the given statement in 5 different ways conveying the same meaning.
- Rewrite the given statements in the form of ‘if….then’
- Write the converse and contrapositive of the given statements.
- Combine the given statements using if and only if.

**Exercise 29 D**

This exercise 29D has 5 questions in which you have to:

- Prove the given statement true or false, using the method of contrapositive.
- Prove the given statement true or false, giving a counter-example.
- Prove the given statement true or false, using a contradiction method.

### Benefits of RS Aggarwal Class 11 Chapter 29

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