A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

A Genral Election in Loksabha - Teachoo.jpg

Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(๐‘‰ 1 , ๐‘‰ 2 ) โˆถ ๐‘‰ 1 , ๐‘‰ 2 ∈ ๐ผ and both use their voting right in general election – 2019}

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Question 1

Two neighbors X & Y ∈ I. X exercised his voting right while Y did not cast her vote in general election- 2019. Which of the following is true?
(a) (X, Y) ∈ R
(b) (Y, X) ∈ R
(c) (X, X) ∉ R
(d) (X, Y) ∉ R

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Question 2

Mr. ’๐‘‹’ and his wife ‘๐‘Š’ both exercised their voting right in general election -2019. Which of the following is true?
(a) both (X, W) and (W, X) ∈ R
(b) (X, W) ∈ R but (W, X) ∉ R
(c) both (X, W) and (W, X) ∉ R
(d) (W, X) ∈ R but (X, W) ∉ R

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Question 3

Three friends F 1 , F 2 and F 3 exercised their voting right in general election-2019, then which of the following is true?
(a) (F 1 , F 2 ) ∈ R, (F 2 , F 3 ) ∈ R and (F 1 , F 3 ) ∈ R
(b) (F 1 , F 2 ) ∈ R, (F 2 , F 3 ) ∈ R and (F 1 , F 3 ) ∉ R
(c) (F 1 , F 2 ) ∈ R, (F 2 , F 2 ) ∈ R but (F 3 , F 3 ) ∉ R
(d) (F 1 , F 2 ) ∉ R, (F 2 , F 3 ) ∉ R and (F 1 , F 3 ) ∉ R

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Question 4

The above defined relation R is __________
(a) Symmetric and transitive but not reflexive
(b) Universal relation
(c) Equivalence relation
(d) Reflexive but not symmetric and transitive

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Question 5

Mr. Shyam exercised his voting right in General Election – 2019, then Mr. Shyam is related to which of the following?
(a) All those eligible voters who cast their votes
(b) Family members of Mr. Shyam
(c) All citizens of India
(d) Eligible voters of India

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  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Serial order wise

Transcript

Question A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation โ€˜Rโ€™ is defined on I as follows: R = {(๐‘‰1, ๐‘‰2) โˆถ ๐‘‰1, ๐‘‰2 โˆˆ ๐ผ and both use their voting right in general election โ€“ 2019} Question 1 Two neighbors X & Y โˆˆ I. X exercised his voting right while Y did not cast her vote in general election- 2019. Which of the following is true? (a) (X, Y) โˆˆ R (b) (Y, X) โˆˆ R (c) (X, X) โˆ‰ R (d) (X, Y) โˆ‰ R Given R = {(๐‘‰1, ๐‘‰2) โˆถ ๐‘‰1, ๐‘‰2 โˆˆ ๐ผ and both use their voting rights} Since X voted, and Y did not vote So, we can write (X, Y) โˆ‰ R Therefore, So, the correct answer is (d) Question 2 Mr. โ€™๐‘‹โ€™ and his wife โ€˜๐‘Šโ€™ both exercised their voting right in general election -2019. Which of the following is true? (a) both (X, W) and (W, X) โˆˆ R (b) (X, W) โˆˆ R but (W, X) โˆ‰ R (c) both (X, W) and (W, X) โˆ‰ R (d) (W, X) โˆˆ R but (X, W) โˆ‰ R Given R = {(๐‘‰1, ๐‘‰2) โˆถ ๐‘‰1, ๐‘‰2 โˆˆ ๐ผ and both use their voting rights} Since X voted, and W also voted Therefore, both (X, W) โˆˆ R and (W, X) โˆˆ R So, the correct answer is (a) Question 3 Three friends F1, F2 and F3 exercised their voting right in general election-2019, then which of the following is true? (a) (F1, F2) โˆˆ R, (F2, F3) โˆˆ R and (F1, F3) โˆˆ R (b) (F1, F2) โˆˆ R, (F2, F3) โˆˆ R and (F1, F3) โˆ‰ R (c) (F1, F2) โˆˆ R, (F2, F2) โˆˆ R but (F3, F3) โˆ‰ R (d) (F1, F2 ) โˆ‰ R, (F2, F3) โˆ‰ R and (F1, F3) โˆ‰ R Given R = {(๐‘‰1, ๐‘‰2) โˆถ ๐‘‰1, ๐‘‰2 โˆˆ ๐ผ and both use their voting rights} Since all 3 friends F1, F2 and F3 voted Therefore, (F1, F2) โˆˆ R, (F2, F3) โˆˆ R and (F1, F3) โˆˆ R So, the correct answer is (a) Question 4 The above defined relation R is __________ (a) Symmetric and transitive but not reflexive (b) Universal relation (c) Equivalence relation (d) Reflexive but not symmetric and transitive Given R = {(๐‘‰1, ๐‘‰2) โˆถ ๐‘‰1, ๐‘‰2 โˆˆ ๐ผ and both use their voting rights} Check reflexive Here, (V , V) โˆˆ R So, R is reflexive, Check symmetric If V1 and V2 both use their voting rights Then, if (V1, V2) โˆˆ R , then (V2, V1) โˆˆ R. Hence , R is symmetric. Check transitive If (V1, V2) and (V2, V3) โˆˆ R , then (V1, V3) โˆˆ R. So, R is transitive Since R is reflexive, symmetric & transitive. Therefore, R is an equivalence relation. So, the correct answer is (c) Question 5 Mr. Shyam exercised his voting right in General Election โ€“ 2019, then Mr. Shyam is related to which of the following? (a) All those eligible voters who cast their votes (b) Family members of Mr. Shyam (c) All citizens of India (d) Eligible voters of India Given R = {(๐‘‰1, ๐‘‰2) โˆถ ๐‘‰1, ๐‘‰2 โˆˆ ๐ผ and both use their voting rights} So, Mr. Shyam will be related to all eligible voters who casted their votes So, the correct answer is (a)

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.