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Set theory - worksheet

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  • 1. SN Kansagra School Set Theory – Work sheet Academic Year 2012 – 2013Std : 7 and 8 PBL TeamQ1. Which of the following collections of objects are sets? 1. All planets in the solar system 2. All fast boys in the class 3. All dishonest businessmen in Rajkot 4. All children of you class who are taller than 5 feet 5. All whole numbers less than 20Q2. State whether the set will be a finite set or an infinite set: 1. Set of integers 2. {x | x Є N, x > 1000} 3. Set of all points on the circumference of the circle 4. Set of all points on a line 5. {x | x Є W, x < 250}Q3. Describe the following sets in a set builder form: 1. A = {5,6,7,8,9,10} 2. B = {2, -2} 3. X = {44, 46, 48, 50, 52} 4. M = { } 5. G = { Rajkot, Jamnagar, Bhavnagar, Junagadh} ଵ ଵ ଵ ଵ ଵ ଵ 6. R = {1, ଶ , ଷ , ସ , ହ , ଺ , ଻ } 7. O = {Atlantic, Arctic}Q4. Write the following sets in roster form 1. B = { x | x Є W, x ≥ 7} 2. Y = { x | x = (2n + 1), n Є W, n ≤ 5} 3. T = { x | x is a two digit number , the sum of whose digits is 8} 4. S = { x | x is a prime number, 5 < x < 50 } ଵ 5. J = { x | x = ௡ , n Є N , N < 5}Q5. Are the following sets an empty set or not? 1. A = { x | x Є N, x + 5 = 5} 2. S = { 0 } 3. G = { x | x is an even prime number} 4. Q = { x | x Є W, x + 2 < 2 }Q6. If A = { 2,4,6,8,10}, B = {8,10,12}, C = {2,4,8}, D = {10, 12}, find the values of: 1. ࣈ 2. A’ 3. B’ 4. A ∩ B Page 1 of 2Prepared by Kapil BHATIA – PBL Unit
  • 2. 5. A ᴜ B 6. n (C) 7. n (D) 8. n (C ∩ D) 9. n (C ᴜ B) 10. (A ᴜ C) ‘ 11. (B ∩ D) ‘Q7. Frame two examples of Equal Sets and Equivalent Sets.Q8. Find the power sets for Set C where C = {2,4,6}Q9. List the elements of each of the following sets as per the set builder form. ࣈ = {x : x Є N , x < 50} A = { x : x2 Є ࣈ } B = { x : x = n2, n Є N } C = { x : x is a factor of 3}Also state whether each of the following is true or false. (i) A⊆B (ii) A=B (iii) A↔B (iv) B↔C (v) n(A) = n(C)Q10. Let A = {b,c,d,e} and B = {d,e,f,g} be two subsets of the universal set ࣈ = {b,c,d,e,f,g} Verify whether 1. (A ᴜ B) ‘ = (A’ ∩ B’) 2. (A ∩ B) ‘ = (A’ ᴜ B’) Page 2 of 2Prepared by Kapil BHATIA – PBL Unit