Set Theory & Algebra: how many ordered pairs

Question

Let $n(A)$ denotes the number of elements in set $A$. If $n (A) = p$ and $n(B) = q$, then how many ordered pairs $(a, b)$ are there with $a∈A$ and $b∈B$?

(a) $p^2$

(b) $p\times q$

(c) $p+q$

(d) $2^{pq}$

Answer 1

Take any two sets and try to make ordered pair..
A ={1,2,3,4,5....n}
B = {1,2,3,4,....n}
{(a,b)} = {(1,1) (1,2) (1,3)....(1,n) (2,1) (2,2)....(2,n)........(n,n)}

|{(a,b)}| = p*q

Answer 2

No of ordered pairs will be pq ( every element of A can be combine with every element of q)

Comments

Need a little bit explanation Pls.

---

fix an element from $p$ set and make its ordered pair with every other element of $q$.

Doing this for all $p$ elements will give $p \times q$ ordered pairs.