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?

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.

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

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.

because

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

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.

(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...}

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

Anita Gupta
answered
Jan 03, 2020

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

This discussion on 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 planec){x : 6 + 2x 5x + 3, x N}d)Set of smallest whole numberCorrect answer is 'D'. Can you explain this answer? is done on EduRev Study Group by JEE Students. The Questions and
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