<p>Consider the set&nbsp;\(F = \{\text{Peter}, \text{John}, \text{Mark}\hspace{0.15em}\}\) and the set&nbsp;\(S = \{\text{Luke}, \text{Mary}, \text{Esther}\hspace{0.15em}\}\). In this scenario, it turns out that:</p>
<ol class="num-list"><li><div class="list-item-paragraph">Luke and Mary are children of Mark.</div></li><li><div class="list-item-paragraph">Esther is the daughter of Peter.</div></li></ol>
<p>Let&nbsp;\(R\) be the relation between \(F\) and \(S\) that depicts the parent-child relation.</p>
<p>In general, \((p,c) \in R\) if and only if&nbsp;\(p\) is a parent of \(c\). We may sometimes write \(pRc\) in short for&nbsp;\((p,c) \in R\). We may also draw a diagram to show this relation \(R\).</p>
<p>From the given information, we can express:</p>
<p style="text-align: center">\[R = \{(\text{Mark}, \text{Luke}), (\text{Mark}, \text{Mary}), (\text{Peter}, \text{Esther})\}.\]</p>
<p>We can also draw a relation diagram to represent this relation \(R\):</p>
<p>We can also draw a relation diagram to represent this relation \(R\):</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1779529620978-ddtwsmgtoea.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Note that for a relation, it is not obliged that every element on the left is linked to some element on the right. It is also not required that a relation satisfies the condition that for every element on the left there is only one arrow emerging from it.</p>

Consider the set \(F = \{\text{Peter}, \text{John}, \text{Mark}\}\) and the set \(S = \{\text{Luke}, \text{Mary}, \text{Esther}\}\). In this scenario, it turns out that:

Let \(R\) be the relation between \(F\) and \(S\) that depicts the parent-child relation.

In general, \((p,c) \in R\) if and only if \(p\) is a parent of \(c\). We may sometimes write \(pRc\) in short for \((p,c) \in R\). We may also draw a diagram to show this relation \(R\).

From the given information, we can express:

\[R = \{(\text{Mark}, \text{Luke}), (\text{Mark}, \text{Mary}), (\text{Peter}, \text{Esther})\}.\]

We can also draw a relation diagram to represent this relation \(R\):

Note that for a relation, it is not obliged that every element on the left is linked to some element on the right. It is also not required that a relation satisfies the condition that for every element on the left there is only one arrow emerging from it.

Functions

International Baccalaureate Higher Level Mathematics

An illustration of relation between two sets of people

An illustration of relation between two sets of people