List all the bijections from A into B.a) A={q,r,s} and B={2,3,4}b) A={1,2,3,4} and B={5,6,7,8}

Answer:The list of bijections from A into B are shown below.Step-by-step explanation:A function f is called one-to-one or injective, if and only if[tex]f(x)=f(y)\Rightarrow x = y[/tex]for all x and y in the domain of f.A function f from X to Y is called onto or surjective, if and only iffor every element y∈Y there is an element x∈X with f(x)=y.If a function is one-one and onto, then it is called bijective.Part (a):A={q,r,s} and B={2,3,4}We need to find all the bijections from A into B.(1) [tex]A\rightarrow B=\{(q,2),(r,3),(s,4)\}[/tex](2) [tex]A\rightarrow B=\{(q,2),(r,4),(s,3)\}[/tex](3) [tex]A\rightarrow B=\{(q,3),(r,2),(s,4)\}[/tex](4) [tex]A\rightarrow B=\{(q,3),(r,4),(s,2)\}[/tex](5) [tex]A\rightarrow B=\{(q,4),(r,2),(s,3)\}[/tex](6) [tex]A\rightarrow B=\{(q,4),(r,3),(s,2)\}[/tex]Part (b):A={1,2,3,4} and B={5,6,7,8}We need to find all the bijections from A into B.(1) [tex]A\rightarrow B=\{(1,5),(2,6),(3,7),(4,8)\}[/tex](2) [tex]A\rightarrow B=\{(1,5),(2,6),(3,8),(4,7)\}[/tex](3) [tex]A\rightarrow B=\{(1,5),(2,7),(3,6),(4,8)\}[/tex](4) [tex]A\rightarrow B=\{(1,5),(2,7),(3,8),(4,6)\}[/tex](5) [tex]A\rightarrow B=\{(1,5),(2,8),(3,6),(4,7)\}[/tex](6) [tex]A\rightarrow B=\{(1,5),(2,8),(3,7),(4,6)\}[/tex](7) [tex]A\rightarrow B=\{(1,6),(2,5),(3,7),(4,8)\}[/tex](8) [tex]A\rightarrow B=\{(1,6),(2,5),(3,8),(4,7)\}[/tex](9) [tex]A\rightarrow B=\{(1,6),(2,7),(3,5),(4,8)\}[/tex](10) [tex]A\rightarrow B=\{(1,6),(2,7),(3,8),(4,5)\}[/tex](11) [tex]A\rightarrow B=\{(1,6),(2,8),(3,5),(4,7)\}[/tex](12) [tex]A\rightarrow B=\{(1,6),(2,8),(3,7),(4,5)\}[/tex](13) [tex]A\rightarrow B=\{(1,7),(2,6),(3,5),(4,8)\}[/tex](14) [tex]A\rightarrow B=\{(1,7),(2,6),(3,8),(4,5)\}[/tex](15) [tex]A\rightarrow B=\{(1,7),(2,5),(3,6),(4,8)\}[/tex](16) [tex]A\rightarrow B=\{(1,7),(2,5),(3,8),(4,6)\}[/tex](17) [tex]A\rightarrow B=\{(1,7),(2,8),(3,6),(4,5)\}[/tex](18) [tex]A\rightarrow B=\{(1,7),(2,8),(3,5),(4,6)\}[/tex](19) [tex]A\rightarrow B=\{(1,8),(2,6),(3,7),(4,5)\}[/tex](20) [tex]A\rightarrow B=\{(1,8),(2,6),(3,5),(4,7)\}[/tex](21) [tex]A\rightarrow B=\{(1,8),(2,7),(3,6),(4,5)\}[/tex](22) [tex]A\rightarrow B=\{(1,8),(2,7),(3,5),(4,6)\}[/tex](23) [tex]A\rightarrow B=\{(1,8),(2,5),(3,6),(4,7)\}[/tex](24) [tex]A\rightarrow B=\{(1,8),(2,5),(3,7),(4,6)\}[/tex]