Assignment -1
Grade Class 12
Question:
<p>Let A = {2, 3, 4, 5, …, 17, 18}. Let <span class="math-tex">\(\simeq\)</span> be the equivalence relation on A <span class="math-tex">\(\times\)</span> A, cartesian product of A with itself, defined by (a, b) <span class="math-tex">\(\simeq\)</span> (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is</p>
<p style="display:inline">5</p>
<p style="display:inline">6</p>
<p style="display:inline">7</p>
<p style="display:inline">4</p>
Step-by-Step Solution
Key Concept: The equivalence class of (a, b) under the relation ad = bc consists of all pairs (x, y) in A × A that maintain the same ratio x/y = a/b.
<p>let (3, 2) <span class="math-tex">\(\simeq\)</span> (x, y)<br />
<span class="math-tex">\(\Rightarrow\)</span> 3y = 2x<br />
This is possible in the cases:<br />
x = 3, y = 2<br />
x = 6, y = 4<br />
x = 9, y = 6<br />
x = 12, y = 8<br />
x = 15, y = 10<br />
x = 18, y = 12<br />
Hence total pairs are 6</p>
Correct Answer: B