📝 Sets
Q) Which of the following are sets? Justify your answer
a) The collection of all the months of a year beginning with the letter J.
a) The collection of all the months of a year beginning with the letter J.
b) The collection of the ten most talented writers of India.
c) A team of eleven best cricket batsmen of the world
d) The collection of all boys in your class.
e) The collection of all-natural numbers less than 100.
f) A collection of novels written by the writer Munshi Prem Chand.
g) The collection of all even integers.
h) The collection of questions in this Chapter.
i) A collection of the most dangerous animals in the world.
Q) Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol `\in` or `\notin` in the blank spaces:
a) 5. . .A
b) 8 . . . A
c) 0. . .A
d) 4. . . A
e) 2. . .A
f) 10. . .A
Q) Write the following sets in roster form:
a) A = {`x : x` is an integer and `–3 \leq x < 7`}
b) B = {`x : x` is a natural number less than 6}
c) C = {`x : x` is a two-digit natural number such that the sum of its digits is 8}
d) D = {`x : x` is a prime number which is divisor of 60}
e) E = The set of all letters in the word TRIGONOMETRY
f) F = The set of all letters in the word BETTER
Q) 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}
Q) Examine whether the following statements are true or false:
(i) { a, b } `⊄`{ b, c, a }
(ii) { a, e } `⊂`{ `x : x` is a vowel in the English alphabet}
(iii) { 1, 2, 3 } `⊂` { 1, 3, 5 }
(iv) { a } `⊂` { a, b, c }
(v) { a } `⊂` { a, b, c }
(vi) { `x : x` is an even natural number less than 6} `⊂` { `x : x` is a natural number which divides 36}
Q) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
(i) {3, 4}`⊂` A
(ii) {3, 4} `\in` A
(iii) {{3, 4}}`⊂` A
(iv) 1 `\in` A
(v) 1 `⊂` A
(vi) {1, 2, 5} `⊂` A
(vii) {1, 2, 5} `\in` A
(viii) {1, 2, 3} `⊂` A
(ix) `\phi \in` A
(x) `\phi ⊂` A
(xi) `{\phi} ⊂` A
Q) If `A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }`and `D = { 7, 8, 9, 10 };` find
(i) `A \cup B`
(ii) `A \cup C`
(iii) `B \cup C`
(iv) `B \cup D`
(v) `A \cup B \cup C`
(vi) `A \cup B \cup D`
(vii) `B \cup C \cup D`
Q) If `A = {x : x` is a natural number }, `B = {x : x` is an even natural number}, `C = {x : x` is an odd natural number}and `D = {x : x` is a prime number }, find
(i) `A \cap B`
(ii) `A \cap C`
(iii) `A \cap D`
(iv) `B \cap C`
(v) `B \cap D`
(vi) `C \cap D`
Q) Write the set `{x : x` is a positive integer and `x ^2
< 40}` in the roster form.
Q) Write the set `{1/2, 2/3, 3/4, 4/5, 5/6,6/7}` in the set-builder form
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