Let $A=\{1,2\}$ and $B=\{3,4\} .$ Write $A \times B .$ How many subsets will $A \times B$ have? List them.
Let $A=\{1,2\}$ and $B=\{3,4\} .$ Write $A \times B .$ How many subsets will $A \times B$ have? List them.
$A=\{1,2\}$ and $B=\{3,4\}$
$\therefore A \times B=\{(1,3),(1,4),(2,3),(2,4)\}$
$\Rightarrow n(A \times B)=4$
We know that if $C$ is a set with $n(C)=m,$ then $n[P(C)]=2^{m}$
Therefore, the set $A \times B$ has $2^{4}=16$ subsets. These are
$\varnothing,\{(1,3)\},\{(1,4)\},\{(2,3)\},\{(2,4)\},\{(1,3)(1,4)\}$
$,\{(1,3),(2,3)\}$
$\{(1,3),(2,4)\},\{(1,4),(2,3)\},\{(1,4)(2,4)\},\{(2,3)(2,4)\}$
$\{(1,3),(1,4),(2,3)\},\{(1,3),(1,4),(2,4)\},\{(1,3),(2,3),(2,4)\}$
$\{(1,4),(2,3),(2,4)\},\{(1,3),(1,4),(2,3),(2,4)\}$
Similar Questions
Let $A = \{1, 2, 3, 4, 5\}; B = \{2, 3, 6, 7\}$. Then the number of elements in $(A × B) \cap (B × A)$ is
Let $A = \{1, 2, 3, 4, 5\}; B = \{2, 3, 6, 7\}$. Then the number of elements in $(A × B) \cap (B × A)$ is
$A = \{1,2,3,4......100\}, B = \{51,52,53,...,180\}$, then number of elements in $(A \times B) \cap (B \times A)$ is
$A = \{1,2,3,4......100\}, B = \{51,52,53,...,180\}$, then number of elements in $(A \times B) \cap (B \times A)$ is
Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find
$(A \times B) \cup(A \times C)$
Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find
$(A \times B) \cup(A \times C)$
If $A = \{ x:{x^2} - 5x + 6 = 0\} ,\,B = \{ 2,\,4\} ,\,C = \{ 4,\,5\} ,$ then $A \times (B \cap C)$ is
If $A = \{ x:{x^2} - 5x + 6 = 0\} ,\,B = \{ 2,\,4\} ,\,C = \{ 4,\,5\} ,$ then $A \times (B \cap C)$ is
If $A = \{ 1,\,2,\,3,\,4\} $; $B = \{ a,\,b\} $ and $f$ is a mapping such that $f:A \to B$, then $A \times B$ is
If $A = \{ 1,\,2,\,3,\,4\} $; $B = \{ a,\,b\} $ and $f$ is a mapping such that $f:A \to B$, then $A \times B$ is