Question

For any three sets given as: $A=\{1,2,3\};B=\{4,5,6\}\&C=\{6,7,8\}.$ Select the correct statements.

• A. $A\times (B-C)=\left\{\right(1,6),(2,6),(3,6\left)\right\}$
• B. $B-C=\{4,5\}$
• C. $A\times B=\left\{\right(a,b):\forall a\in A\&b\in B\}$
• D. $A\times C=\left\{\right(c,a):\forall c\in C\&a\in A\}$

Answer 1

Answer: (B), (C)

$A\times B=\left\{\right(a,b):\forall a\in A\&b\in B\}$

Given three sets: $A=\{1,2,3\};B=\{4,5,6\}\&C=\{6,7,8\}$
Now, $B-C=\{4,5,6\}-\{6,7,8\}=\{4,5\}$
Also, $A\times B=\left\{\right(a,b):\forall a\in A\&b\in B\}$
Similarly, $A\times C=\left\{\right(a,c):a\in A\&c\in C\}$
And $A\times (B-C)$
$=\{1,2,3\}\times \left(\right\{4,5,6\}-\{6,7,8\left\}\right)=\{1,2,3\}\times \{4,5\}=\left\{\right(1,4),(1,5),(2,4),(2,5),(3,4),(3,5\left)\right\}$