Question

If $A=\{5,7\},B=\{7,9\}$ and $C=\{7,9,11\},$ find $(A\times B)\cup (A\times C)$

• A. $\left\{\right(5,7),(9,9),(5,11),(7,7),(7,9),(7,11\left)\right\}$
• B. $\left\{\right(5,7),(5,9),(5,11),(7,7),(7,9),(7,11\left)\right\}$
• C. $\left\{\right(5,5),(5,9),(5,11),(7,7),(7,9),(7,11\left)\right\}$
• D. none of these

Answer 1

Answer: (B)

$\left\{\right(5,7),(5,9),(5,11),(7,7),(7,9),(7,11\left)\right\}$

Product of two sets is found by forming ordered pairs by multiplying every element of the first set with the second set.
So, $A\times B=$ { $(5,7),(5,9),(7,7),(7,9)$ }
And $A\times C=$ { $(5,7),(5,9),(5,11),(7,7),(7,9),(7,11)$ }
Union of two sets has all the elements of both the sets.
So, $(A\times B)\cup (A\times C)=$ { $(5,7),(5,9),(5,11),(7,7),(7,9),(7,11)$ }