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}
$\therefore \quad A \times(B-C)=\{1,2,3\} \times\{4\}=\{(1,4),(2,4),(3,4)\}$
Now,
$\begin{array}{l}A \times B=\{1,2,3\} \times\{4\}=\{(1,4),(2,4),(3,4)\} \\
\text { and, } A \times C=\{1,2,3\} \times\{5\}=\{(1,5),(2,5),(3,5)\}\end{array}$
$\therefore \quad(A \times B)-(A \times C)=\{(1,4),(2,4),(3,4)\} \ldots \ldots . .( ii )$
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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