Question

If $A=\{5,7\},B=\{7,9\}$ and $C=\{7,9,11\},$ find :

Whether $A\times (B\cup C)=(A\times B)\cup (A\times C)holdstrueornot?$

Answer 1

Union of two sets has all the elements of both the sets
$=>B\cup C=$ { $7,9,11$ }
Product of two sets is the set of ordered pairs formed by mapping every element from the first set to every element of the second set.
So, $A\times (B\cup C)=$ { $(5,7),(5,9),(5,11),(7,7),(7,9),(7,11)$ }
Also,
And $A\times B=$ { $(5,7),(5,9),(7,7),(7,9)$ }
Now, $A\times C=$ { $(5,7),(5,9),(5,11),(7,7),(7,9),(7,11)$ }
And, $(A\times B)\cup (A\times C)=$ { $(5,7),(5,9),(5,11),(7,7),(7,9),(7,11)$ }
Hence, $A\times (B\cup C)=(A\times B)\cup (A\times C)holdstrue$