Find Sets A and B if (x,1), (y,2), (z,1) are in A × B
Question
Let \( A \) and \( B \) be two sets such that
\[ n(A)=3 \quad \text{and} \quad n(B)=2. \]
If
\[ (x,1),(y,2),(z,1)\in A\times B, \]
write \( A \) and \( B \).
Solution
From the ordered pairs, the first components are:
\[ x,y,z \]
Therefore,
\[ A=\{x,y,z\} \]
The second components are:
\[ 1,2 \]
Therefore,
\[ B=\{1,2\} \]
Hence,
\[ \boxed{A=\{x,y,z\},\quad B=\{1,2\}} \]