1. **Problem:** Decide whether each set of ordered pairs is a function from $W = \{a, b, c, d\}$ into $W$. A function must assign exactly one output in $W$ for each input in $W$. 2. **Recall:** A set of ordered pairs is a function if and only if no input element appears more than once with different outputs. 3. **(a)** $\{(b, a), (c, d), (d, a), (c, d), (a, d)\}$ - Inputs: $b, c, d, c, a$ - Note $c$ appears twice but both map to $d$, so no conflict. - All inputs $a,b,c,d$ appear once with unique outputs. - **Conclusion:** This is a function. 4. **(b)** $\{(d, d), (c, a), (a, b), (d, b)\}$ - Input $d$ appears twice with outputs $d$ and $b$. - This violates the function rule. - **Conclusion:** Not a function. 5. **(c)** $\{(a, b), (b, b), (c, d), (d, b)\}$ - Inputs $a,b,c,d$ each appear once. - **Conclusion:** This is a function. 6. **(d)** $\{(a, a), (b, a), (a, b), (c, d)\}$ - Input $a$ appears twice with outputs $a$ and $b$. - Violates function rule. - **Conclusion:** Not a function. **Final answers:** - (a) Function - (b) Not a function - (c) Function - (d) Not a function