MHT CET · Maths · Sets and Relations
If \(\mathrm{A}=\{x, y, z\}, \mathrm{B}=\{1,2\}\), then the total number of relations from set \(\mathrm{A}\) to set \(\mathrm{B}\) are
- A 64
- B 16
- C 32
- D 8
Answer & Solution
Correct Answer
(A) 64
Step-by-step Solution
Detailed explanation
It is given that \(A=\{x, y, z\}\) and \(B=\{1,2\} .\)
\(\therefore A \times B=\{(x, 1),(x, 2),(y, 1),(y, 2),(z, 1),(z, 2)\}\)
Since \(n(A \times B)=6\), the number of subsets of \(A \times B\) is \(2^{6} .\)
Therefore, the number of relations from \(A\) to \(B\) is \(2^{6} .\)
\(\therefore A \times B=\{(x, 1),(x, 2),(y, 1),(y, 2),(z, 1),(z, 2)\}\)
Since \(n(A \times B)=6\), the number of subsets of \(A \times B\) is \(2^{6} .\)
Therefore, the number of relations from \(A\) to \(B\) is \(2^{6} .\)
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