Question

Which of the following pairs is/are a disjoint set(s)?

• A. A = {x : x is an even prime number}
  B = {x : x is an even number less than 10}
• B. C = {x : x is a solution of $x^2-25=0$ }
  D = {x : x is an integer such that x < 5}
• C. E = {x : x is a whole number and a multiple of 7 less than 20}
  F = {x : x is a natural number and a multiple of 3}
• D. G = {x : x is a natural number}
  H = {x : x is not a positive integer}

Answer 1

Answer: (C), (D)

The correct options are
C E = {x : x is a whole number and a multiple of 7 less than 20}
F = {x : x is a natural number and a multiple of 3}
D G = {x : x is a natural number}

H = {x : x is not a positive integer}
A = {x : x is a even prime number}={2}
B = {x : x is a even number less than 10}={2,4,6,8}
2 is common element in both set A and set B. Therefore, set A and set B are not disjoint sets.

C = {x : x is a solution of $x^2-\mathrm{25\; =\; 0}$}={-5, 5}
D = {x : x is an integer such that x < 5} = {...-3, -2, -1, 0,1,2,3,4}
-5 is common element in both set C and set D. Therefore, set C and set D are not disjoint sets.

E = {x : x is a whole number and multiple of 7 less than 20} ={0, 7, 14}
F = {x : x is a natural number and a multiple of 3} = {3,6,9,12,15,18,21,24,....}
No element is common in both set E and set F. Therefore, set E and set F are disjoint sets.

G = {x : x is a natural number} = {1,2,3,4,....}
H = {x : x is an not a positive integer} = {.....,-3,-2,-1,0}
No element is common in both set G and set H. Therefore, set G and set H are disjoint sets.