NCERT Class 11-Math՚S Exemplar Chapter 1 Sets CBSE Board Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 7:

Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.

(i) All the students who study Mathematics study English, but some students who study English do not study Mathematics.

(ii) There is no student who studies both Mathematics and English.

(iii) Some of the students study Mathematics but do not study English, some study English but do not study Mathematics, and some study both.

(iv) Not all students study Mathematics, but every students studying English studies Mathematics.

Answer:

Since all of the students who study mathematics study English, but some students who study English do not study Mathematics.

Therefore,

Thus the Venn Diagram is.

Fig-1.4-Venn Diagram

(ii) Since there is no student who study both English and Mathematics

Hence,

Fig-1.5-Venn Diagram

(iii) Since there are some students who study both English and Mathematics, some English only and some Mathematics only.

Thus, the Venn Diagram is

Fig-16-Venn Diagram

(iv) Since every student studying English studies Mathematics.

Hence

Mathematics

Question 8:

For all sets A, B and C

Is ?

Justify your statement.

Answer:

No. consider the following sets A, B and C:

Now

And

Therefore,

Question 9:

Use the properties of sets to prove that for all the sets A and B

Answer:

We have