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2.Relations and Functions
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मान लीजिए कि $A =\{1,2\}$ और $B =\{3,4\} . A \times B$ लिखिए। $A \times B$ के कितने उपसमुच्चय होंगे ? उनकी सूची बनाइए
Option A
Option B
Option C
Option D
Solution
$A=\{1,2\}$ 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
$\varnothing,\{(1,3)\},\{(1,4)\},\{(2,3)\},\{(2,4)\},\{(1,3)(1,4)\}$
$,\{(1,3),(2,3)\}$
$\{(1,3),(2,4)\},\{(1,4),(2,3)\},\{(1,4)(2,4)\},\{(2,3)(2,4)\}$
$\{(1,3),(1,4),(2,3)\},\{(1,3),(1,4),(2,4)\},\{(1,3),(2,3),(2,4)\}$
$\{(1,4),(2,3),(2,4)\},\{(1,3),(1,4),(2,3),(2,4)\}$
Standard 11
Mathematics
