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}
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B
C = {x : x is a solution of x225 = 0 }
D = {x : x is an integer such that x < 5}
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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}
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D
G = {x : x is a natural number}
H = {x : x is not a positive integer}
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Solution

## 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 x2âˆ’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.

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