# RD Sharma Class 11 Chapter 31 Solutions (Mathematical Reasoning)

RD Sharma Solutions for Class 11 Maths Chapter 31 – Mathematical Reasoning are created to help you solve all the exercise questions of the chapter without any problems. In this chapter, we shall be covering the mathematical deduction, difference between sentences and statements and whether they are true or false. There are a total of 6 exercises with 37 questions extensively covering all the possible questions that can come in the exams.

In RD Sharma Class 11 Chapter 31, there are a total of 6 exercises with 37 questions extensively covering all the possible questions that can come in the exams. Mathematical reasoning is also an important subject because a lot of questions in competitive exams come from this topic. Also being a comparatively simple topic this creates an opportunity to increase your marks in exams if you prepare well.

The pattern of questions is in such a way that they usually give you a scenario and ask questions related to it. One main thing that has to be noted is that a sentence can be true or false but not both at the same time. Experts at Instasolv have tried to explain all of these most logically and easily. ** **RD Sharma Solutions for Class 11 will help you understand every concept and solve questions easily.

## Topics covered in RD Sharma Solutions for Class 11 Chapter 31 – Mathematical Reasonings

Understanding mathematical induction in the previous chapter, which is also a part of mathematical reasoning; now it’s time to understand mathematical deduction, which hereby is called mathematical reasoning.

Mathematical reasoning can be explained by a simple example. Let’s say a football is either white or blue, and if it is not blue, then from that logic, it leads us to a hypothesis that football must definitely be white. Logic is the reasoning conducted with strict principles of validity.

A statement can either be true or false, but not both at the same time. And all of these statements make mathematical reasoning. There are different types of statements, for example; simple statements, compound statements, universal statements, conditional statements and existential statements.

Let’s take an example,

There are 10 days in a week.

Now, since we know that there are only 7 days in any week, therefore, this sentence is false. However, since it is very clear that it is false, therefore we can say that the above example is a statement.

Another example of deductive reasoning can be the following,

If X=Y and Y=Z then we can say X=Z.

In exercises some sentences will be given and based on them we have to deduct if they are statements or not. For example, is the moon round? The above is an interrogative sentence therefore it is not a statement.

The negation of a statement is another topic from which the questions can come is a negation of a statement, it means that when we deny a statement.

Let’s take an example,

i: the USA is a country

The negation of this statement is,

It is not a case that the USA is a country or It is false that the USA is a country or the USA is not a country.

If i is a statement, then the negation of i is also a statement and can be denoted by ~i and read as “not i”

We may also be asked to find the components in compound statements. Let’s just take an example.

I: There is something wrong with the tap or the pipe.

The above statement tells us that there is some problem with the tap or the pipe.

This statement is divided into two small statements.

P: there is something wrong with the tap

Q: there is something wrong with the pipe

Above, the word ‘or’ is the component of joining two small sentences.

We may also be asked to find the components of a compound statement and if they are true or not.

For example, Jammu and Srinagar are the capital of Jammu and Kashmir.

The component statements of the above statement are:

Jammu is the capital of Jammu and Kashmir

Srinagar is the capital of Jammu and Kashmir

Since both the cities are the capital of Jammu and Kashmir, therefore the above statement holds true.

However, we have to remember that the word ‘and’ is not always used as a conjunction. For example, hydrogen and oxygen can be removed by chemical processes. The above statement is just one and not a compound statement.

**Discussion on the Exercises of RD Sharma Solutions for Class 11 Chapter 31 – Mathematical Reasonings**

There are six exercises full of good quality questions for a thorough understanding of mathematical reasoning. Let us have a look at the distribution of exercises in RD Sharma Class 11 Maths Solutions Chapter 31:-

- Exercise 31.1 has 2 questions divided into 19 sub-questions and asks whether the specified sentences are statements or not.
- Exercise 31.2 has 5 questions divided into 17 sub-questions and focuses and not the negation of the sentences.
- Exercise 31.3 has 4 questions divided into 17 sub-questions and focuses on the compound statements and its components.
- Exercise 31.4 has 4 sub-questions in 2 parts and asks to give negation of mathematical statements
- Exercise 31.5 has 28 subparts in 4 questions and asks about the converse of the statements.
- Exercise 31.6 has 8 questions and 15 sub-questions and is a mixture of all the above topics.

### Benefits of RD Sharma Solutions for Class 11 chapter 31 Mathematical Reasonings by Instasolv

In this chapter, Instasolv has tried to provide the simplest language for you to understand mathematical reasoning and the deduction behind it. With the questions provided by RD Sharma and solutions provided by Instasolv you will be able to understand this topic and score good marks in your exams.