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Maths-

General

Easy

Question

Let $A$ be the set of all students in a school. A relation $R$ is defined on $A$ as follows:
$" a R b$ iff $a$ and $b$ have the same teacher”

Reflexive
Symmetric
Transitive
Equivalence

The correct answer is: Equivalence

We have,
$n open parentheses A intersection stack B with minus on top close parentheses equals 9 comma n open parentheses stack A with minus on top intersection B close parentheses equals 10$ and $n open parentheses A union B close parentheses equals 24$
$rightwards double arrow n open parentheses A close parentheses minus n open parentheses A intersection B close parentheses equals 9 comma n open parentheses B close parentheses minus n open parentheses A intersection B close parentheses equals 10$ and, $n open parentheses A close parentheses plus n open parentheses B close parentheses minus n open parentheses A intersection B close parentheses equals 24$
$rightwards double arrow n open parentheses A close parentheses plus n open parentheses B close parentheses minus 2 n open parentheses A intersection B close parentheses equals 19$ and $n open parentheses A close parentheses plus n open parentheses B close parentheses minus n open parentheses A intersection B close parentheses equals 24$
$rightwards double arrow n open parentheses A intersection B close parentheses equals 5$
$therefore n open parentheses A close parentheses equals 14$ and $n open parentheses B close parentheses equals 15$
Hence, $n open parentheses A cross times B close parentheses equals 14 cross times 15 equals 210$

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Set builder form of the relation
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