ધારો કે $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ અને $D=\{5,6,7,8\},$ તો નીચેનાં પરિણામો ચકાસો : $A \times(B \cap C)=(A \times B) \cap(A \times C)$

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, $A \times(B \cap C)=(A \times B) \cap(A \times C)$