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 $B \times D$
Similar Questions
If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?
If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?
If $A = \{ a,\,b\} ,\,B = \{ c,\,d\} ,\,C = \{ d,\,e\} ,\,$ then $\{ (a,\,c),\,(a,\,d),\,(a,\,e),\,(b,\,c),\,(b,\,d),\,(b,\,e)\} $ is equal to
If $A = \{ a,\,b\} ,\,B = \{ c,\,d\} ,\,C = \{ d,\,e\} ,\,$ then $\{ (a,\,c),\,(a,\,d),\,(a,\,e),\,(b,\,c),\,(b,\,d),\,(b,\,e)\} $ is equal to
Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find
$A \times(B \cup C)$
Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find
$A \times(B \cup C)$
If $A = \{2, 3, 5\}, B = \{2, 5, 6\},$ then $(A -B) × (A \cap B)$ is
If $A = \{2, 3, 5\}, B = \{2, 5, 6\},$ then $(A -B) × (A \cap B)$ is
If $A = \{1, 2, 4\}, B = \{2, 4, 5\}, C = \{2, 5\},$ then $(A -B) × (B -C)$ is
If $A = \{1, 2, 4\}, B = \{2, 4, 5\}, C = \{2, 5\},$ then $(A -B) × (B -C)$ is