Which of the following is not an empty set?
  • a)
    {x : x is a multiple of 7, x < 7, x ∈ N}
  • b)
    Set of common points of two parallel lines in a plane
  • c)
    {x : 6 + 2x > 5x + 3, x ∈ N}
  • d)
    Set of smallest whole number
Correct answer is 'D'. Can you explain this answer?

JEE Question

By Abhishek Dubey · Dec 12, 2019 ·JEE
14 Answers
Lakshya Agnihotri answered Dec 29, 2019
D is right answer.
for a- since x belongs to natural no. and x《7 i.e.
x=(1 2 3 4 5 6 ) and since all these aren't multiple of 7 so a is wrong.
for b - 2 planes can't have common points as they are parallel and they never intersect so they can't have a common point .
for c- for every natural no. c is not true as for x=1 LHS=RHS , for x=2 LHS 《RHS ... and so on...
for d- smallest whole no. is 0 which tells that it is not an empty set.
so ans. is d.

Banu Lucky answered Jan 09, 2020
Every multiple of 7 is always greater than 7
there will be no common points for two parallel lines as the y don't intersect each other
the given inequality ,6+2x< />
hence set of smallest whole number is not empty as smallest whole number is 0

Shashank Jaiswal answered May 26, 2018
As, the set of Whole numbers is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...};
So, according to the set of whole numbers above, the smallest whole number should be "0" and therefore the set of smallest whole number is not empty.

Dr Stephen Strange answered Jan 07, 2020
Correct answer is (A)
because
multiple of 7 can't be smaller than 7 itself.

Kartik Swami answered Jan 07, 2020
Smallest whole number is zero which can't be a empty set

Prateek Raj answered 3 weeks ago
Correct answer is d because option a, b, c, are empty set.
(A) - In table of 7 any number is not less than 7 when x belongs to natural number. ex:- 7,14,21,28,35,42,49,56,etc thus, (empty set)

(B) - In these parallel lines: == or I I . There were no intersection points or no common points as you see. ( distance between two or more parallel lines remain always equal) . thus, (empty set)

(C) - as you put the values of x, where x is a natural number
then you get the same value for x=1 but for greater than 1
you get the value of 5x+3 more than 6+2x which is not satisfying by the given condition. thus, (empty set)

(D) - whole numbers : 0,1,2,3,4,5,6,7,8,9,10,11,etc
set of smallest whole number is 0 - {0}.thus,(Singleton set)
not an empty set.

Sagar Pandey answered Jan 23, 2020
Option 1,2and3clearly an empty set but option d is not an empty set because it contains element:
w={0,1,2,3,4,5,6,7...}

Vansh Bhardwaj answered Dec 12, 2019
D- Set of smallest whole no. which has definite value

Sahil Rana answered Jan 08, 2020
Correct answer is option 'D'

Anita Gupta answered Jan 03, 2020
D is right because there is only 1 smallest whole no. so it can't be empty set

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