(Solved): Will upvote you :') Please give worked solutions and explanation, thank you! Consider the fol ...

Will upvote you :') Please give worked solutions and explanation, thank you!

Consider the following relations on the sets \( A=\{1,2,3,4,5\} \) and \( B=\{1,2,3,4\} \). (a) Suppose \( f_{1}=\{(1,2),(2,4),(3,3),(4,2),(5,1)\}, f_{1}: A \rightarrow B \) is a function. Which of the following are true? Indicate all correct answers. \[ \begin{array}{l} f_{1} \subseteq A \times B . \\ f_{1} \subseteq B \times A . \end{array} \] \( f_{1} \) is surjective. \( f_{1} \) is injective. (b) Suppose \( f_{2}=\{(1,3),(2,2),(3,4),(4,1)\}, f_{2}: B \rightarrow A \) is a function. Which of the following are true? Indicate all correct answers. \[ \begin{array}{l} f_{2} \subseteq A \times B . \\ f_{2} \subseteq B \times A . \end{array} \] \( f_{2} \) is injective. \( f_{2} \) is surjective. (c) Suppose \( f_{3} \subseteq B \times A \) is defined by \[ f_{3}=\{(1,3),(2,1),(3,2),(x, 4)\} . \] Indicate all values of \( x \) for which this is not a function.