Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that
$A \times(B \cap C)=(A \times B) \cap(A \times C)$
Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that
$A \times(B \cap C)=(A \times B) \cap(A \times C)$
To verify: $A \times(B \cap C)=(A \times B) \cap(A \times C)$
We have $B \cap C=\{1,2,3,4\} \cap\{5,6\}=\varnothing$
$\therefore \mathrm{L .H. S .}=A \times(B \cap C)=A \times \varnothing=\varnothing$
$A \times B=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)\}$
$A \times C=\{(1,5),(1,6),(2,5),(2,6)\}$
$\therefore R H S=(A \times B) \cap(A \times C)=\varnothing$
$\therefore L.H.S.=R.H.S.$
Hence, $A \times(B \cap C)=(A \times B) \cap(A \times C)$
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 $A = \{ 2,\,4,\,5\} ,\,\,B = \{ 7,\,\,8,\,9\} ,$ then $n(A \times B)$ is equal to
If $A = \{ 2,\,4,\,5\} ,\,\,B = \{ 7,\,\,8,\,9\} ,$ then $n(A \times B)$ 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
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 $A$ and $B$ be two sets such that $n(A)=3$ and $n(B)=2 .$ If $(x, 1),(y, 2),(z, 1)$ are in $A \times B$, find $A$ and $B$, where $x, y$ and $z$ are distinct elements.
Let $A$ and $B$ be two sets such that $n(A)=3$ and $n(B)=2 .$ If $(x, 1),(y, 2),(z, 1)$ are in $A \times B$, find $A$ and $B$, where $x, y$ and $z$ are distinct elements.
If $R$ is the set of all real numbers, what do the cartesian products $R \times R$ and $R \times R \times R$ represent?
If $R$ is the set of all real numbers, what do the cartesian products $R \times R$ and $R \times R \times R$ represent?