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
125 Answers
Shruti Dubey answered Dec 09, 2019
D

Shalini Nawariya answered Mar 25, 2020
Yes D will be the right answer because in all the statement , set will not consist any element satisfying given condition except option D as 0 is the smallest whole number as per given .

Shweta Singh answered May 03, 2020
It is not defined that how many numbers are smallest whole number as it is given in question to write the set of smallest whole number.

Yashwanth Kota answered 2 weeks ago
Option D is correct because in D "0" is an element so it's not an empty set

Shashmith Shashmith answered Mar 24, 2020
D is correct answer

Anupam Jain answered Apr 18, 2020
Yes ,buddy correct ans is 'D' Because it have element {0}
so it is correct

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.

Tarun Mahawar answered Apr 15, 2020
Set of smallest whole number is {0}, which is a non empty set.So, correct answer is option is (D).

Peter Parker answered Apr 03, 2020
Option D is correct.

Nisha Sharma answered May 22, 2020
Answer is D( Set of smaller whole number)

Aman Choudhary answered 3 weeks ago
Because the smallest number set is not actually it is an imznary number called negative infinite

Raveendra Chandagani answered May 29, 2020
O is small est whole no

Amrit Raj Garg answered 4 days ago
I m felling sleepy so I won't answer

Aditi Sharma answered Jun 29, 2020
D option is correct
the reason is smallest whole number is zero
and zero and fie are different things fie represents null set whereas zero may or may not be element of any sets
hence in this case the answer is {0}
therefore it's not empty set
hope you guys understood it :-)

Vandana Gupta answered Mar 23, 2020
Smallest whole number cannot make a set because it is single term and single terms do not make sets.

Lahari Mothukuri answered Jun 01, 2020
If you see option( a ) x can be 7,14,21and so on but according to given condition these numbers are not less than 7 hence it is an empty set

if you see option (b) two parallel lines cannot intersect each other so there is no common point hence it is an empty set

if you see otion (c) 6+2x>5x+3 can only be possible when x is a negative number but according to given condition x should be natural number hence it is an empty set

if you see option (d) whole numbers are {0,1,2,3,4,and so on} in this smallest whole number is {0} hence it is not an empty set. can also say it as singleton set

Nishtha Hari answered Jun 13, 2020
In option (a) we write it in roster form;
{ } or phi .....phi is member of every set so it will come in every set.
in option (b) we write it in roster form;
{ } or phi as there is no common point between two parallel lines, they can never intersect.
in option (c) in roster form;
{ } or phi....if we take natural no. 1
6+2(1)=8. 5(1)+3=8
as 8 cannot be big no. than itself so ans. is phi
but in opt (d);
{0}, phi .....as phi is member of every set so there is phi as well as 1 member so it is not considered as a null set hence opt (d) is correct one.

Bhargav Sompura answered Jun 26, 2020
D is correct option as it has one element [0] in it and all other are empty set.

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

Shivam Kumar answered Jun 22, 2020
0,1,2,3,4...are comes whole number ,
so it cannot be a null set

Prateek Raj answered Feb 13, 2020
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.

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

Anjali Malviya answered Jul 08, 2020
Yess
set of smallest whole number = { 0 }
which is not an empty set
no. of elements in above set is 1

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

Raja Kotni answered 4 weeks ago
Option d is the correct because remaining options are empty sets

Web2karn answered 2 weeks ago
Because smallest whole number is 0 and that is a null set

Vivek Sagarwal answered Apr 08, 2020
Set of smallest number is start from 0

Shikha Singh Shikha Sing answered Jul 07, 2020
D is a correct option

Tanisha Kalia answered Jun 14, 2020
D is the right answer

Waseem Raja Wasi answered Apr 03, 2020
0 is a samalest whole number . therefore it's not empty set {0}

Devansh Raj answered May 31, 2020
(D) is correct answer

Diya Bhardwaj answered May 11, 2020
D option is correct

Anjali Kumari answered May 27, 2020
It is because smallest whole number is 0 which is null or empty set

Sarika Bharti answered May 01, 2020
Correct option is D because it has an element 0 while in all other options a null set became.

Saravanan J answered Jun 30, 2020
(a) answer is right

Chinmay Mahajan answered Mar 23, 2020
Set of smallest whole number can't be defined because smallest whole number is 0 and so to which limits the number are involved can't be explained hence d is the correct explanation

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...}

Rahul Kumar answered Jun 10, 2020
(a) x € fi
(b) empty set
(c) 6 + 2x > 5x + 3
or,. 3 > 3x
or ,
x < />
now,
x € fi
(d) if we see 1 is the smallest whole number for 2 , 3 etc similar for all thus it's set = {0 , 1 , 2 , 3 , .....}
which is not empty set.
hence d is the correct because

Abhi Gupta answered May 21, 2020
Answer is 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

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

Anilkumar Bharti answered Jun 05, 2020
Set of smallest whole no conatains 0 as its element...

option c could have been a non empty set until it's an integer and it is mentioned natural numbers...so an empty set
option b ....two parallel lines have no solution so an empty set for common point...
similarly in option a x cannot be the multiple of 7 until it's negative and integers are not allowed so also an empty set

Asiya Anjum answered Jun 01, 2020
Set of smallest whole number is 0.,so it is not an empty set.....
hence option D is correct

Varshitha Bittu answered Jun 18, 2020
D
x<7=0 but="" not="" natural="" number="" so="" empty="" set="">
2.parallel lines never coincide so empty set
3.on solving we get x<1=0 but="" does="" not="" belongs="" to="" natural="" number="" so="" empty="" set="">
4.smallest whole number is 0 so it is not a empty set

Khirod Mondal answered Jun 04, 2020
Yes D option is right because one element is exist in this set . 0 is the smallest whole number

Avula Vivekanandam answered Apr 20, 2020
Yes D option is right, because in above three options are null set, fourth option is not null set because smallest whole number is 0 (zero)

Rajendra Singh Bhandari answered May 20, 2020
All option contain no elements in there sets
but option D contain a number 0 in its set so D should be correct ans

Ananta Kumari answered Jul 04, 2020
Smallest whole number is 0,which is count as one element of the set

Ajinkya Kutarmare answered 3 weeks ago
Correct answer is D option

Shashank Shekhar answered 2 weeks ago
D because
smallest whole number is is zero so the set will exist

Abbrar .m answered 2 weeks ago
Yes d is the correct answer.

Jayant Kumar answered 2 weeks ago
D is correct , because it is smallest whole number and it's set is possible as { { },{0} }. And rest all are empty set.

Ujwala Desu answered May 19, 2020
Option D is the ans bcuz smallest whole number ois "0" therefore cardinal number of the set is 1 but not zero ....so it can't be an empty set

Kotakids Notebook answered May 25, 2020
D is not an empty set as it contains 0 smallest whole numbers as elements.

Sathya Moorthi Sathya Mo answered May 26, 2020
Because the smallest whole number set is {0}. This is not an empty set

Harsh Gujalwar answered May 27, 2020
Set of smallest whole no. is zero i.e not empty while others are

Sachin Yadav answered Jun 03, 2020
A is correct answer

Aadarsh Shriniwas answered Jun 15, 2020
D because 0 is the smallest whole number .
So the set will not be empty .

Deepti Mahajan answered Jun 15, 2020
Smallest whole number is 0
that means this set has 1 element so this is not empty set

Mannat Miglani answered Jul 05, 2020
Yes d, bcz it will be a singleton set containing 0 in it.

Harsh Verma answered 2 weeks ago
The set is-. 0, 1, 2,..... which is a finite set and not a null set....

Komal Patel answered Jul 06, 2020
Options no. D is correct

Preeti Shukla answered 4 weeks ago
Here option D is correct because in this option it is said that set of smallest whole number which is never be a empty set that is 0 is the smallest whole number. So,{0} is the required set which is not empty .
THANKYOU

Damini Tijare answered May 12, 2020
If we find elements in the set then we find that all a,b,c have no elements but for option d there is some element so option d is correct.

Shresthi Shelke answered May 12, 2020
Coz smallest whole number is zero and zero is considered as element of set .. D is the answer

Mahammad Shaikh answered May 07, 2020
Because the smallest whole number is zero.
and in the set zero number show empty set therefore correct option is D

Aparna Cshaiva answered Jun 08, 2020
Because set if smallest whole number is (0). therefore a number exist in this set, it is not a void set

Isha Mishra answered May 23, 2020
Ans D is not an empty set, as zero is the smallest whole no, rest of the options are empty sets,
a) there is no multiple of 7 less than 7
b) parallel lines have no common point
c)empty set

Ashok Kumar answered May 22, 2020
D...is correct because
0 is the smallest whole no.

Shashi Bhushan answered May 26, 2020
As empty set is set of no elements present in it.
since sets belongs to the smallest whole no that is which is not an empty set.A={0}, set a has one element in its.
Hence D is correct answer.

Aluru Pragna answered Jun 29, 2020
A) {x: x is a multiple of 7 , x<7,x belongs="" to="">
there is no such that number exists because it is said that x is multiple of 7 and x<7 and="" that="" x="" should="" be="" a="" natural="" number="">
so it is an empty set

b)set of common points of two parallel lines in a plane
the two parallel lines does not intersects at any point
so it is an empty set

c){x :6+2x > 5x+3 ,x belongs to N}
6+2x > 5x+3 = 3 > 3x = 1>x = x<1>
there is such that number exists because x is a natural number . Natural numbers starts from 1 to infinity. But in the expression x<1. so="" there="" is="" no="" such="" that="">
so it is an empty set

d)set of smallest whole number
if we take 5 as an whole number. the smallest whole numbers less than 5 are 0,1,2,3,4
so it is not an empty set

so answer for this question is (d) option

Ravindra Kumar Yadav answered Jun 28, 2020
A aur c to dekh ke bata sakte aur c ko solve karne ke bad ans nahi aa raha main to d ko he karuga waise option reject kare to a aur b ho sakte aur c ko check karlo

Mukul Bhatia answered 3 weeks ago
D is the correct answer because the set of smallest whole no. can be written as {0} which is not a null set. Rest of the followings are all examples of null set

Bibhabasu Dutta answered 2 weeks ago
Here, D = Set of smallest whole number.
Since we know zero is the smallest whole number, then D={0} So D is not an empty set, hence it is the correct answer.

Ramesh Sinha answered 3 weeks ago
D because d is a singleton sey

Pavan Kishore answered yesterday
Set of smallest whole number contains {0},so it is not an empty set

Gourav Mahore answered Jun 07, 2020
Whole number [0 ∞]

so smallest whole number is 0

Aaradhaya Singh answered Jun 07, 2020
Yes i can explain
as a set of smallest whole number is 0 hence it is an empty
set.