Question

Q1. Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b- is the empty relation and R′ = ,(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Answer 1

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GIVEN

• Let A be the set of all students of a boys school.

• Two relation R and R ' is A given by

• R = {(a, b) : a is sister of b}

• R′ = {(a, b) : the difference between heights of a and b is less than 3 meters}

TO PROVE

• R is a Empty Relation

• R' is an Universal Relation

CALCULATION

ANSWER TO QUESTION : 1

Here A is the set of all students of a boys school

The relation R on A is given by

R = {(a, b) : a is sister of b}

Since A is the set of all students of a boys school

So there is no girl student in the school.

So there is no chance of having sister of a boy

Therefore R contains no element

Hence R is a Empty Relation

ANSWER TO QUESTION : 2

Here A is the set of all students of a boys school

The relation R ' in A given

R′ = { (a, b) : the difference between heights of a and b is less than 3 meters}

Here 3 metre = 9. 8 ft

Therefore the difference between heights two students must be is less than 3 meter

So there is no pair of students such that difference between heights of them is greater than or equal to 3 meter

So R' is an Universal Relation

Hence proved

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LEARN MORE FROM BRAINLY

Given set A = {1, 2, 3... 10).

Relation R is defined in set A as

R = {(a, b) € A × A : a = 2b }

Then range of relation R is

Then range of relation R ishttps://brainly.in/question/23567484