Logic, Sets and Real Number System: Class 11 Mathematics Solutions

Logic, Sets and Real Number System : Class 11 Mathematics Solutions

  Chapter - 1  
Logic, Sets and Real Number System

Logic, Sets and Real Number System is the first chapter of class 11 mathematics according to 2079 syllabus. In this chapter we will learn about Sets and Real Number from logical point of view. Before we move towards the excercise let's have a look at the main content of this chapter. 

1.1 Logic
1.2 Statements
1.3 Truth value and truth table
1.4 Logical Connectives
1.5 Sets
1.6 Theorems based on Set Operation
1.7 Real Number System
1.8 Representation of a number in a real line
1.9 Interval
1.10 Absolute Value

1.1 Logic

The dictionary meaning of logic is the science of reasoning. In mathematics, we deal with various theorems and formulae. The different procedures used in giving the proofs of various theorems and formulae are based on sound reasoning. The study of such procedures based on sound reasoning is known as a logic.

In logic, we use symbols for words, statements and their relations to get the required result. Hence, logic is known as mathematical logic or symbolic logic.

1.2 Statements

An assertion expressed in words or symbols, which is either true or false but not both at the same time, is known as a statement. Some examples of statements are given below: 
i) Water is essential for health.
ii) 2+4=6
iii) A quadrilateral has three sides.
(i), (ii) and (iii) are statements as (i) and (ii) are true but (iii) is false.

1.3 Truth value and truth table

A truth or the falsity of a statement is known as its truth value. T or F is the truth value of a statement according as it is true or false. A table presenting the truth values of the component statements together with the truth values of their compound statement, is known as the truth table.

1.4 Logical Connectives

Compound statements are made from the simple statements by using the words or phrase like "and", "or", "If ...... then" and "If and only if" and they are known as logical connectives or simply connectives.

1.5 Sets

The word "set" is known to carry the same meaning as the words collection, class and aggregate. However a set may be thought of as a well-defined list or collection of material objects such as books and pens or conceptual objects such as numbers and points. Each object of a set is called an element or member of the set.

1.6 Theorems based on Set Operation

Combinations of various relations and operations defined on sets give rise to a number of interesting and useful results. Some of them are so fundamental that they are considered as the basic laws of set algebra. We discuss them under the following four categories.
a) Properties of Inclusion and Equality Relations
b) Properties of Unions
c) Properties of Intersections
d) Miscellaneous Properties

1.7 Real Number System

The union of the set of rational and irrational numbers is known as the set of real numbers. So, by the set of real numbers, we have the set of natural numbers, the set of integers, the set of rational numbers and the set of irrational numbers.

The set of real numbers are denoted by R. Thus the set of rational and irrational numbers taken together, form a new system of numbers known as the real number system.

1.8 Representation of a number in a real line

The set of real numbers can be beautifully represented by means of the points on a straight line which is called a real line.

1.9 Interval

Let a and b be two numbers on the real line. Then the set of points on the real line between a and b is known as an interval, a and b are known as the end points of the interval. An interval is denoted by 1. An interval may or may not include the end points. So, we get the following four different types of intervals.
i) Open-interval
ii) Closed interval
iii) Left open interval
iv) Right open interval

1.10 Absolute Value

Let x denote any real number. The absolute value (or modulus or numerical value) of x. written as |x|, is a non-negative real number defined by ;
|x|= [x, if x >= 0]
|x|= [- x, if x < 0]

 Exercise - 1.1

This PDF contains all the solutions of class 11, logic, sets and real numbers system chapter. 

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Is Class 11 Mathematics Guide Helpful For Student ?

I have published this Notes for helping students who can't solve difficult maths problems. Student should not fully depend on this note for completing all the exercises. If you totally depend on this note and simply copy as it is then it may affect your study.

Student should also use their own will power and try to solve problems themselves. You can use this mathematics guide PDF as a reference. You should check all the answers before copying because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.

How to secure good marks in Mathematics ?

As, you may know I'm also a student. Being a student is not so easy. You have to study different subjects simultaneously. From my point of view most of the student are weak in mathematics. You can take me as an example, I am also weak in mathematics. I also face problems while solving mathematics questions . 

If you want to secure good marks in mathematics then you should practise them everyday. You should once revise all the exercise which are already taught in class. When you are solving maths problems, start from easy questions that you know already. If you do so then you won't get bored.

Maths is not only about practising, especially in grade 11 you to have the basic concept of the problem. When you get the main concept of the problem then you can easily any problems in which similar concept are applied. 

When your teacher tries to make the concept clear by giving examples then all students tries to remember the same example but you should never do that. You can create your own formula which you won't forget later.

If you give proper time for your practise with proper technique then you can definitely score a good marks in your examination. 

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