If $A imes B = \{(p, q), (p, r), (m, q), (m, r)\}$, find $A$ and $B$.

Question

If $A 	imes B = \{(p, q), (p, r), (m, q), (m, r)\}$, find $A$ and $B$.

Accepted Answer

A. $A = \{p, m\}$, $B = \{q, r\}$

$A$ = set of first elements = $\{p, m\}$. $B$ = set of second elements = $\{q, r\}$. Verify: $\{p, m\} 	imes \{q, r\}$ produces exactly the four given pairs.

Answer

$A = \{q, r\}$, $B = \{p, m\}$

Answer

$A = \{p, q, m, r\}$, $B = \phi$

Answer

$A = \{p\}$, $B = \{m\}$

If $A \times B = \{(p, q), (p, r), (m, q), (m, r)\}$, find $A$ and $B$.