1. **Problem Statement:** (a) Determine which function from the given options is bijective between sets $P = \{10, 20, 30\}$ and $Q = \{5, 10, 15, 20\}$. 2. **Recall:** A function is **bijective** if it is both **one-to-one (injective)** and **onto (surjective)**. - **Injective:** Each element of $P$ maps to a unique element in $Q$ (no duplicates in outputs). - **Surjective:** Every element of $Q$ is mapped by some element in $P$. 3. **Check each function:** - A: $f = \{(10,5), (10,10), (10,15), (10,20)\}$ maps 10 to multiple values, so not a function. - B: $f = \{(10,5), (20,10), (30,15)\}$ maps each element of $P$ to a unique element in $Q$. Outputs are $5, 10, 15$. - C: $f = \{(20,5), (20,10), (30,10)\}$ 20 maps to two values, not a function. - D: $f = \{(10,5), (10,10), (20,15), (10,20)\}$ 10 maps to multiple values, not a function. 4. **Is B bijective?** - Injective: Yes, all outputs distinct. - Surjective: $Q$ has $5, 10, 15, 20$ but $20$ is not mapped, so not onto. **Conclusion:** None of the given options is bijective. --- **Final answer for (a):** No function listed is bijective.