Sets miscellaneous exercise

Gujarat Board Gujarat Board Textbook Solutions Class 11 Maths Chapter 1 Sets Miscellaneous Exercise Question 1. Decide, among the following sets, which are the subsets of one and another: A = . i.e., A ∩ B, A ∩ C and B ∩ C are non-empty sets. ∴ (A ∩ B) ∩ C = (2) ∩ (1, 3) A ∩ B ∩ C = ϕ Question 13. In a survey of 600 students in a school, 150 students were found to be drinking Tea and 225 drinking Coffee, 100 were drinking both Tea and Coffee. Find how many students were drinking neither Tea nor Coffee? Solution: Here, n(T) = 150, n(C) = 225, n(T ∩ C) = 100. Also, we know that n(T ∪C) = n(T) + n(C) – n(T ∩C) = 150 + 225 – 100 = 275. Total no. of students = 600. ∴ No. of students who neither take tea nor coffee = 600 – n(T ∪C) = 600 – 275 = 325. Question 14. In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group? Solution: Here, n(H) = 100, n(E) = 50 and n(H ∩ E) = 25. We know that n(H ∪E) = n(H) + n(E) – n(H ∩E) = 100 + 50 – 25 = 125. Question 15. In a survey of 60 people, it was found that 25 people read Newspaper H, 26 read Newspaper I, 26 read Newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find? • The number of people who read at least one of the newspapers. • The number of people who read exactly one newspaper. Solution: Clearly, 1. No. of people who read at least one newspaper = (8 + 8 + 10 +...

Rajasthan Board RBSE Class 11 Maths Chapter 1 Sets Miscellaneous Exercise Question 1. Solution of equation x 2 + x – 2 = 0 in Roster form is: (A) Hence, option (D) is correct. Question 2. are the square of 1, 2, 3, 4, 5,… respectives. Hence, option (C) is correct. Question 4. Which set is infinite of the following: (A) (A ∩ B)’ = A’ ∪ B’ Question 27. Using Venn diagrams, represent the sets given below: (i) (A ∪ B) ∩ C (ii) (A ∩ B) ∪ C (iii) A’ ∪ B’ (iv) (A ∪ B)’ Solution: (i) (A ∪ B) ∩ C Firstly we shade the area of A and B by horizontal lines which represent A ∪ B. Then we shade the area of (A ∪ B) ∪ C by vertical lines. The cross shaded area represents the area of (A ∪ B) ∩ C. (ii) (A ∩ B) ∩ C Firstly we shade the common area of A and B which represent (A ∩ B) after that we shade the area of (A ∩ B) and C which represent (A ∩ B) ∪ C. (iii) A’ ∪ B’ A’ = U – A, B’ = U – B Horizontal shaded region A’ vertical shaded region B’ Hence, whole shaded region = A’ ∪ B’ (iv) (A ∪ B)’ The shaded region is (A ∪ B)’ Hence Proved. Question 28. With the help of Venn diagram prove that: (i) (A ∪ B)’ = A’ ∩ B’ (ii) (A ∩ B)’ = A’ ∪ B’ Solution: (i) (A ∪ B)’ = A’ ∩ B’ Shaded region (A ∪ B)’ Horizontal shaded A’ Vertical shaded region B’ Cross shaded region A’ ∩ B’ Hence (A ∪ B)’ = A’ ∩ B’ (ii) (A ∩ B)’ = A’ ∪ B’ Shaded region (A ∩B)’ Horizontal shaded A’ Vertical shaded B’ Whole shaded region A’ ∩ B’ Hence Proved.

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Exercise 1.3 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Ex 1.3 provided in NCERT Textbook. • • • • • • • • • • • • • • • • • • Chapter 1: • अध्याय 1: Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20. Q.1: Fill in the blanks properly using ⊂ and ⊄. (i). सार्वत्रिक समुच्चय हैं। Filed Under: