Answers (Solutions)

Practical  No.14

14) Sets and Relations

Practical Session No. 14-Sets and Relations

11th-Math-Practical-No-14-Sets-and-Relations-answer-solution-Balbharati-Maharashtra-Board-HSC-Board

Practical Session No. 14

Sets and Relations

1. For the following sets, if possible i) list the elements of A ii) Find n(A)

iii) write using interval notation iv) sketch on number line

a) {}:39AxNx=∈−≤≤ b) {}:39AxZx=∈−≤≤ c) {}:39AxRx=∈−≤≤

d) {}:47AxRx=∈≤< e) {}:2AxQx=∈−≤ f) {}:7AxZx=∈<

2. Use separate Venn Diagrams and shade the regions for the following:

a) A b) 'B c) AB∪ d) 'AB∪ e) 'AB∪ f) ''AB∪ g) ()'AB∪ h) ()''AB∪ i) AB∩ j) 'AB∩ k) 'AB∩ l) ''AB∩ m) ()'AB∩ n) ()''AB∩

3. Use separate Venn Diagrams and shade the regions for the following:

a) A b) 'B c) AC∪ d) 'BC∪ e) 'ABC∪∪

f) ''BCC∪∪ g) ()'ABC∪∩ h) ()''ABC∪∪ i) BAC∩∩ j) ()'CBA∩∪

4. In a group of 50 students, 20 study subject A, 25 study subject B and 20 study subject C. 10 study both A and B, 5 study both B and C, 7 study both A and C. 2 study all three subjects.

a) show this information on Venn diagram

b) find the number of students who study i) A only ii) B or C iii) A but not C iv) none of A , B or C.

5. Show all possible relations from {},Aab=to {}5,6B= using Arrow diagram. Find among them the relations that are i) One-One relation ii) Onto relations iii) Null relation iv) Universal relation.

6. Plot AB×and BA×on XY plane, if

a) {}{}:,15;:,3AxxNxByyWy=∈≤≤=∈<

b) {}{}:,14;:,13AxxRxByyZy=∈<≤=∈−≤<

7. Let R be the relation defined by (){},:26,,10,RxyxyxWxyZ=+=∈≤∈ Find i) R ii) Domain of R iii) Co-domain of R iv) Range of R

8. Given the relation ()(){}2,3,3,4R=on set of natural numbers N, add a minimum number of ordered pairs so that the relation is i) reflexive ii) symmetric iii) transitive iv) equivalence.