Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that
$A \times C$ is a subset of $B \times D$
Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that
$A \times C$ is a subset of $B \times D$
To verify: $A \times C$ is a subset of $B \times D$
$A \times C=\{(1,5),(1,6),(2,5),(2,6)\}$
$A \times D=\{(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),$
$(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8)\}$
We can observe that all the elements of set $A \times C$ are the elements of set $B \times D$. Therefore, $A \times C$ is a subset of $B \times D$
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