If $A =(1,2,3), B =\{4\}, C =\{5\}$, then verify that $A \times(B-C)=(A \times B)-(A \times C)$.
✓
Answer
As given in the question we have, $A = \{1, 2, 3\}, B = \{4\}$ and $C = \{5\}$
From set theory, $(B - C) = \{4\}$
$\therefore A \times(B-C)=\{1,2,3\} \times\{4\}=\{(1,4),(2,4),(3,4)\}$
Now,
$A \times B=\{1,2,3\} \times\{4\}=\{(1,4),(2,4),(3,4)\}$
$\text { and, } A \times C=\{1,2,3\} \times\{5\}=\{(1,5),(2,5),(3,5)\}$
$\therefore (A \times B)-(A \times C)=\{(1,4),(2,4),(3,4)\} \ldots \ldots . .( ii )$
From equation $(i)$ and equation $(ii),$ we get
$A \times(B-C)=(A \times B)-(A \times C)$
We can see the equations $(i)$ and $(ii)$ have same ordered pairs.
Hence verified.
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