Sets

17. How many elements has P(A), if A = $?$ ?

16. Write down all the subsets of the following sets

(i) {a}

(ii) {a, b}

(iii) {1, 2, 3}

(iv) $?$

15. Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

(i) {3, 4} $\subset$ A

(ii) {3, 4} $\in$ A

(iii) {{3, 4}} $\subset$ A

(iv) 1 $\in$ A

(v) 1 $\subset$ A

(vi) {1, 2, 5} $\subset$ A

(vii) {1, 2, 5} $\in$ A

(viii) {1, 2, 3} $\subset$ A

(ix) $?\in$ A

(x) $?\subset$ A

(xi) { $?$ } $\subset$ A

14. Examine whether the following statements are true or false:

(i) { a, b } ? { b, c, a }

(ii) { a, e } $\subset$ { x : x is a vowel in the English alphabet}

(iii) { 1, 2, 3 } $\subset$ { 1, 3, 5 }

(iv) { a } $\subset$ { a, b, c }

(v) { a } $\in$ { a, b, c }

(vi) { x : x is an even natural number less than 6} $\subset$ { x : x is a natural number which divides 36}

Class 11 Set Exercise 1.3 Solutions

13. Make correct statements by filling in the symbols $\subset$or ? in the blank spaces :

(i) { 2, 3, 4 } . . . { 1, 2, 3, 4,5 }

(ii) { a, b, c } . . . { b, c, d }

(iii) {x : x is a student of Class XI of your school}. . .{x : x student of your school}

(iv) {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with radius 1 unit}

(v) {x : x is a triangle in a plane} . . . {x : x is a rectangle in the plane}

(vi) {x : x is an equilateral triangle in a plane} . . . {x : x is a triangle in the same plane}

(vii) {x : x is an even natural number} . . . {x : x is an integer}

12. From the sets given below, select equal sets :

A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2}

E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}

11. Are the following pair of sets equal? Give reasons.

(i) A = {2, 3}, B = {x : x is solution of x²+ 5x + 6 = 0}

(ii) A = { x : x is a letter in the word FOLLOW}

(iii) B = { y : y is a letter in the word WOLF}

10. In the following, state whether A = B or not:

(i) A = { a, b, c, d } B = { d, c, b, a }

(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}

(iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x < 10}

(iv) A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }

9. State whether each of the following set is finite or infinite:

(i) The set of lines which are parallel to the x-axis

(ii) The set of letters in the English alphabet

(iii) The set of numbers which are multiple of 5

(iv) The set of animals living on the earth

(v) The set of circles passing through the origin (0,0)

8. Which of the following sets are finite or infinite

(i) The set of months of a year

(ii) {1, 2, 3, . . .}

(iii) {1, 2, 3, . . ., 99, 100}

(iv) The set of positive integers greater than 100

(v) The set of prime numbers less than 99