Q.(i) Let $A = \{1,2,3,4\}$ and $B = \{5,6\}$, with arrows $1\to5$, $2\to5$, $3\to6$, $4\to6$. Classify this function.

For each diagram, check separately whether any element of B is shared by two arrows, and whether every element of B is used, then combine both checks.

Part (i): $1\to5$, $2\to5$, $3\to6$, $4\to6$.

• One-one vs many-one: element $5$ receives two arrows (from $1$ and $2$), and element $6$ also receives two arrows (from $3$ and $4$) — this is many-one.
• Onto vs into: the range is $\{5,6\}$, which equals the co-domain $B=\{5,6\}$ exactly — every element of $B$ is used, so this is onto.
• Bijective? No — a function must be BOTH one-one and onto to be bijective; this one is onto but not one-one, so it is not bijective.

Part (ii): $1\to4$, $2\to5$, $3\to6$ (element $7$ unused).

• One-one vs many-one: the three arrows land on three different elements ($4$, $5$, $6$), no element of $B$ shared by two arrows — this is one-one. …

Assuming a function must be bijective just because it is onto (part i) or just because it is one-one (part ii) — bijective specifically requires BOTH properties together, and each part here deliberately has only one of the two. Also, in part (i), missing that B …