If $P = \{a, b, c\}$ and $Q = \{r\}$, are the products $P \times Q$ and $Q \times P$ equal?
AYes, always equal
BNo — ordered pairs $(a, r)$ and $(r, a)$ are different
CYes, since each has 3 elements
DEqual only if $|P| = |Q|$
Answer & Solution
Correct answer: B. No — ordered pairs $(a, r)$ and $(r, a)$ are different
$P \times Q = \{(a,r),(b,r),(c,r)\}$ vs $Q \times P = \{(r,a),(r,b),(r,c)\}$. The pairs $(a,r) \ne (r,a)$, so the products are different (though they have the same cardinality).
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