Q.Let $A = \{a, b, c\}$ and $B = \{1, 2, 3, 4\}$, with the arrows $a \to 2$, $b \to 4$, $c \to 2$. Is this a function from $A$ to $B$? If so, state its domain, co-domain and range.

Check whether every element of A has exactly one outgoing arrow, then read off the domain, co-domain and range from the diagram.

Step 1 — Check the function conditions. Every element of $A$ — $a$, $b$, $c$ — has exactly one outgoing arrow ($a\to2$, $b\to4$, $c\to2$), and none has more than one. Both conditions for a function are satisfied.

Step 2 — State the domain. The domain is the starting set itself: $\{a, b, c\}$.

Step 3 — State the co-domain. The co-domain is the entire target set as given: $\{1, 2, 3, 4\}$. …

Listing the range as $\{1,2,3,4\}$ (the full co-domain) instead of correctly restricting it to only the elements actually hit by an arrow, $\{2,4\}$. Also, listing $2$ twice in the range because two different elements ($a$ and $ …