Q.Let $A = \{1, 2, 3\}$ and $B = \{4, 5, 6\}$, with the arrows $1\to 4$, $2\to 5$, $3\to 6$. Classify this function as one-one or many-one, and as onto or into. Is it bijective?

Check whether any element of B receives more than one arrow, and whether every element of B is used, then combine both checks to decide bijectiveness.

Step 1 — Check one-one vs many-one. The three arrows land on $4$, $5$, $6$ respectively — three DIFFERENT elements of $B$, no element of $B$ receiving more than one arrow. This is one-one.

Step 2 — Check onto vs into. The range is $\{4,5,6\}$ (every element that received an arrow), and the co-domain is $B = \{4,5,6\}$. Since range $=$ co-domain, every element of $B$ is used — this is onto. …

Concluding "bijective" from just one of the two checks (e.g. seeing that it's one-one and assuming onto follows automatically) — both conditions must be verified independently, since a function can easily be one-one without being onto (see …