If $A=\{a, b, c\}, B=\{b, c, d\}$ and $C=\{a, d, c\}$, then $(A-B) imes(B\cap C)$ is equal to:
(A) $\{(a, d), (c, d)\}$
(B) $\{(a, c), (a, d)\}$
(C) $\{(c, a), (d, a)\}$
(D) $\{(a, c), (a, d), (b, d)\}$

Question

If $A=\{a, b, c\}, B=\{b, c, d\}$ and $C=\{a, d, c\}$, then $(A-B)	imes(B\cap C)$ is equal to:
(A) $\{(a, d), (c, d)\}$
(B) $\{(a, c), (a, d)\}$
(C) $\{(c, a), (d, a)\}$
(D) $\{(a, c), (a, d), (b, d)\}$

Accepted Answer

> [!TLDR]
> A − B = {a}, B ∩ C = {c, d}, so {a} × {c, d} = {(a, c), (a, d)}.

### Step 1 — Set difference
A = {a, b, c}, B = {b, c, d}: elements of A not in B ⇒ A − B = {a}.

### Step 2 — Intersection
B = {b, c, d}, C = {a, d, c}: common elements ⇒ B ∩ C = {c, d}.

### Step 3 — Cartesian product
$$\{a\} 	imes \{c, d\} = \{(a, c), (a, d)\}$$

> [!WARNING]
> Ordered pairs: the first coordinate must come from A − B, so (c, a) and (d, a) are wrong. …

Step 1 — Set difference

Step 2 — Intersection

Step 3 — Cartesian product

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