1. **Stating the problem:** We have sets $A=\{a,b,c,d\}$ and $B=\{5,7,9\}$ and four relations: A. $f=\{(a,1),(b,2),(c,3),(d,4)\}$ B. $g=\{(a,1),(b,1),(c,1),(d,1)\}$ C. $F=\{(a,4),(a,1),(a,2),(a,3)\}$ D. $G=\{(a,4),(b,4),(c,4),(d,4)\}$ We need to determine which of these are functions (mappings) from $A$ to $B$. 2. **Definition of a function:** A relation from $A$ to $B$ is a function if every element in $A$ is related to exactly one element in $B$. 3. **Check each relation:** - For A: The codomain $B$ is $\{5,7,9\}$ but the pairs use $1,2,3,4$ which are not in $B$. So $f$ is not a function from $A$ to $B$ because the outputs are not in $B$. - For B: The pairs are $\{(a,1),(b,1),(c,1),(d,1)\}$, again $1 \notin B$, so $g$ is not a function from $A$ to $B$. - For C: The pairs are $\{(a,4),(a,1),(a,2),(a,3)\}$, multiple outputs for $a$, so it is not a function (violates uniqueness), and also outputs not in $B$. - For D: The pairs are $\{(a,4),(b,4),(c,4),(d,4)\}$, all outputs are $4$ which is not in $B$, so not a function from $A$ to $B$. 4. **Conclusion:** None of the given relations are functions from $A$ to $B$ because their outputs are not elements of $B$ or violate the function rule. **Final answer:** None of A, B, C, or D are functions from $A$ to $B$.