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?

190 Answers

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
Jul 29, 2020

Option D is correct because in D "0" is an element so it's not an empty set

Anupam Jain
answered
Apr 18, 2020

Yes ,buddy correct ans is 'D' Because it have element {0}

so it is correct

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).

Roshni Mohapatra
answered
Sep 13, 2020

As because no other options are valid for sets containing elements...option D is the correct option because this set contains the element 0(the smallest whole number).

Kamali Anandbabu
answered
Sep 10, 2020

Option D is correct.

If u see in option A, multiples of 7 is 7,14, 21, so on.. It is given that x is less than 7, therefore option A is an empty set.

In option B, there is no common points between two parallel lines in a plane because that two lines do not intersect. So this option is also an empty set.

In option C, x should be in negative then only this condition will be satisfied because for example if we put 1 for x it will come like this 8>8, this is not be satisfied. If we put -1 for x it will 4>-2. This can be satisfied but it is given that x belongs to natural number. Therefore this option is also an empty set.

In option D, the set is ( 0, 1, 2, 3, so on..) according to the condition, the set of smallest whole number is (0). Therefore option D is not an empty set.

If u see in option A, multiples of 7 is 7,14, 21, so on.. It is given that x is less than 7, therefore option A is an empty set.

In option B, there is no common points between two parallel lines in a plane because that two lines do not intersect. So this option is also an empty set.

In option C, x should be in negative then only this condition will be satisfied because for example if we put 1 for x it will come like this 8>8, this is not be satisfied. If we put -1 for x it will 4>-2. This can be satisfied but it is given that x belongs to natural number. Therefore this option is also an empty set.

In option D, the set is ( 0, 1, 2, 3, so on..) according to the condition, the set of smallest whole number is (0). Therefore option D is not an empty set.

Aman Choudhary
answered
Jul 23, 2020

Because the smallest number set is not actually it is an imznary number called negative infinite

Sakshi Dombe
answered
Sep 22, 2020

D is the right answer cause here is not given any condition or range cor whole numbers.

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

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

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 :-)

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.

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.

{ } 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.

Kurakula Suryateja
answered
Aug 19, 2020

(D) is the correct answer because smallest whole number is 0 if it is a set it would be like this {0}

if any element in a set it would be a non empty set

so option d is correct

if any element in a set it would be a non empty set

so option d is correct

Dr Stephen Strange
answered
Jan 07, 2020

Correct answer is (A)

because

multiple of 7 can't be smaller than 7 itself.

because

multiple of 7 can't be smaller than 7 itself.

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.

(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.

Manash Hial
answered
Aug 22, 2020

If one knows basic maths too he can easily say first three options are empty set coz no elements fits the conditions. About ans D the smallest whole no is 0 ,so the set is not empty that it is a singleton set with one element 0.

Shaurya Sawai
answered
Sep 15, 2020

Correct answer is d as smallest whole number is 0 so {0} is not a empty set as it contain one element which is 0.

K Sankara Rao
answered
2 weeks ago

Option A is an empty set because there would be no multiple of 7 which is less than 7 and belonging to the set of natural numbers . option b is also an empty set because there would be no common points to 2 parallel lines . option c is also an empty set because if you choose any random number the given statement will also be wrong there fore it is also an empty set.and the last option d the smallest whole number is 0, it is not an empty set ,so d is the right answer

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

set of smallest whole number = { 0 }

which is not an empty set

no. of elements in above set is 1

Abhitej Tiwari
answered
Sep 13, 2020

Surely many find that first 2 options are a void set and 4th consist of { '0' } only

for 3 we can prove it as follows

given -

6+2x > 5x+3 which means

2x > 5x-3 (subtract 3 from both sides) and

x > 5x-3/2

it can be easily seen that this property doesn't hold's good.

and so the set is a null set !!

note: at x= 1 in the given eq.

1is not greater than 1.

it is equal to it.

for 3 we can prove it as follows

given -

6+2x > 5x+3 which means

2x > 5x-3 (subtract 3 from both sides) and

x > 5x-3/2

it can be easily seen that this property doesn't hold's good.

and so the set is a null set !!

note: at x= 1 in the given eq.

1is not greater than 1.

it is equal to it.

Waseem Raja Wasi
answered
Apr 03, 2020

0 is a samalest whole number . therefore it's not empty set {0}

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.

Anjali Kumari
answered
May 27, 2020

It is because smallest whole number is 0 which is null or empty set

Rohit Kumar
answered
Sep 19, 2020

And: (d), as smallest whole number is zero and so it's set contain it's element as zero.

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...}

w={0,1,2,3,4,5,6,7...}

Rahul Kumar
answered
Jun 10, 2020

(a) x â‚¬ fi

(b) empty set

(c) 6 + 2x > 5x + 3

or,. 3 > 3x

or ,

x < />

now,

x â‚¬ 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

(b) empty set

(c) 6 + 2x > 5x + 3

or,. 3 > 3x

or ,

x < />

now,

x â‚¬ 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

Saurabh Rajput
answered
Aug 14, 2020

D is correct answer . it is a set of well defined object because smallest whole number is 0

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

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

hence option D is correct

Anita Gupta
answered
Jan 03, 2020

D is right because there is only 1 smallest whole no. so it can't be empty set

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

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

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

Shashank Shekhar
answered
Jul 26, 2020

D because

smallest whole number is is zero so the set will exist

smallest whole number is is zero so the set will exist

Dazle Roger
answered
Aug 17, 2020

As you that 0 is the smallest whole number and 0 is a empty set so d 8s correct

Jayant Kumar
answered
Jul 29, 2020

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

Cinderella
answered
Sep 16, 2020

Answer is D

because the smallest whole number is 0

so set of smallest whole number will be{0}

which is not empty...hence Option D will be the correct answer.

because the smallest whole number is 0

so set of smallest whole number will be{0}

which is not empty...hence Option D will be the correct answer.