Question

Let \(A\) and \(B\) be two finite sets. If \(n(A) = 7\) and the number of relations from \(A\) into \(B\) is 128, then \(n(B) =\)

• A. 4
• B. 3
• C. 2
• D. 1
• E. 0

Hint:

A relation is any subset of \(A \times B\), so total subsets = \(2^{|A||B|}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Number of relations from \(A\) to \(B\) is \(2^{n(A)\cdot n(B)}\).
Step 2: Detailed Explanation:
Given \(2^{7 \cdot n(B)} = 128 = 2^7\). So \(7 \cdot n(B) = 7 \implies n(B) = 1\).
Step 3: Final Answer:
Option (D).