SETS - Online Class 11 Maths NCERT Solutions

INTERSECTION AND UNION:

The set of elements common to two given sets A and B is known as the intersection and written as A ∩ B. The set of elements appearing in at least one of these sets is called the union, denoted by A ∪ B.

EXAMPLE: Decide which elements ought to belong to each of A ∪ B ∪ C and A ∩ B ∩ C. Then write a compact description of each set using bar notation.

Note that the set operation of intersection corresponds to the logical operation of conjunction. This relationship is made clear by the fact that

A ∩ B = {x | x ∈ A and x ∈ B}.

Similarly, union corresponds to the logical operation of disjunction, since

A ∪ B = {x | x ∈ A or x ∈ B}.

We say that A and B are equal sets, written A = B, if these two sets contain precisely the same elements. One common technique for showing that two sets are equal is to show that every element of the first set must be an element of the second set, and vice-versa.

To establish the set identity A ∩ B = A ∪ B we use these two strategies.

Step one: Let x be any element of the first set; i.e. let x ∈A ∩ B. This means that x “∈ A ∩ B. Since A ∩ B consists of elements in both A and B, if x is not in the intersection then either x “∈ A or x “∈ B, or both. In other words, x ∈ Aor x ∈ B, which means that x ∈ A ∪ B.

Step two: On the other hand, if x ∈ A ∪ B then we know that x ∈ A or x ∈ B, which means that x “∈ A or x “∈ B. Since x is missing from at least one of the sets A or B, it cannot reside in their intersection, hence x “∈ A∩B. Finally, this is the same as x ∈ A ∩ B. Hence, we conclude that the sets A ∩ B and A ∪ Bare indeed equal.

Read complete chapter click SETS - Online Class 11 Maths NCERT Solutions

For better preparations, you can visit www.takshilalearning.com. We offer online and offline courses for the individual subject, as well as group wise for Class 1st to 12th, are also available.

Comments

Magnetic and non-magnetic material Class 6 Science

Magnetic and non-magnetic material Class 6 Science A magnet is a substance that is drawn to certain magnetic materials like iron, cobalt, and nickel. Magnets have the ability to draw iron to them. Natural magnets are rocks that naturally draw iron. Non-magnetic materials include things like wood, rubber, coins, feathers, leather, etc. that are not drawn to iron. Magnet characteristics It pulls magnetic materials, such as iron. The magnet's two ends are referred to as its poles. The magnet's diametrically opposed poles are drawn together. Heating, hammering, or dropping causes it to lose its characteristics. On the basis of properties types of Magnets Temporary magnets are those magnets that are magnetic for only a little duration. Typically, iron, cobalt, or nickel are used to make them. When they are close to the powerful magnet, they act like a magnet. When they are yanked away from the powerful magnet, they stop being magnetic. Permanent magnets are magnets that have magne...

Best Sample papers for Bank PO Exam Download

Sample papers for Bank PO Exam | Question Paper for Bank PO : Institute of banking Personnel Selection (IBPS) Department issued a Notification of IBPS PO 2017 exam announced in October month. IBPS Probationary Officer (PO) Online Application Form process will be begin from July 2017. This is a hard exam for all students so aware of its value. Large number of candidates will participate in this exam. So all candidates should prepare well for it. Check out IBPS, Bank PO Sample papers, Question Paper Pattern, SBI PO Syllabus , IBPS Syllabus and other IBPS PO Preparation 2017 This paper is identical to any Bank PO Question Paper Pattern. Check whole IBPS Bank “PO question paper” subject wise. IBPS (PO) Paper Pattern Analysis with Syllabus and main topics of IBPS Exam 2017. PO Question Paper Pattern, Bank PO sample Papers for IBPS Bank Exam IBPS PO Exam will be conducted at three levels 1st- PO Preliminary Exam 2nd- PO Mains Exam 3rd- PO Common ...

Online/Offline CBSE Coaching Classes for class 9

CBSE Coaching Class 9 :- In a move to make the digital India and Skill India dream into a reality, we are providing the best courses to our students in e-learning mode. Our program consists of entire 9th class syllabus in a fun learning method with various ways like sounds and animations. Our content is in 2-D & 3-D animation for better understanding of students. So That students will be understand every thing clearly and it makes the learning easy and entertaining. We are offering the following subjects for class 9th Standard: Maths Class Physics Class Chemistry Class Biology Class Our E-learning provides the best and trained teachers with highly qualified for the respective subjects, they help to improve the students’ performance and to teach the every concept clear and easy in better way. Our main motive is to help students to learn well and gain more marks with making their basic concept strong and good knowledge base ...

Takshila Learning - Online Tutorials

Search This Blog