Assignment -1
Grade Class 12
Question:
<p><strong>Assertion (A): </strong>The possible number of reflexive relations of a set A whose n(A) = 4 is 2<sup>12</sup>.<br />
<strong>Reason (R): </strong>Number of reflexive relation on a set contain n elements is <span class="math-tex">\(2^{n^2-n}\)</span>.</p>
<p style="display:inline">Both A and R are true and R is the correct explanation of A.</p>
<p style="display:inline">Both A and R are true but R is not the correct explanation of A.</p>
<p style="display:inline">A is true but R is false.</p>
<p style="display:inline">A is false but R is true.</p>
Step-by-Step Solution
Key Concept: The number of reflexive relations on a set with n elements is $2^{n^2-n}$, because all n diagonal pairs $(a, a)$ must be included, leaving $n^2-n$ optional pairs.
<p>Given, n(A) = 4<br />
Total number of reflexive relations = 2<sup>n(n -1)</sup><br />
<span class="math-tex">\(=2^{4 \times 3}\)</span> = 2<sup>12</sup></p>
Correct Answer: A