o Theorem 3.7:: a) Let f be a function from a to B, Inverse relation f- is a function from B to A if only iff is one to one &(b) Let f be an everywhere function from a to B, Inverse relation f-I is an everywhere function from B to A if only if f is one-to-one correspondence. o Proof:(a(1)Iff- is a function, then f is one to one 今 If there exist a,;a2∈ A such that f(a1)=fa2)=b∈B, then a1?=a2 o(2)If f is one to one, then f- is a function 冷∫ is a function Forb∈B, If there exist a1,a2∈ A such that(b,a1)∈f1 and(b, a2)ef-, then a? =a2❖ Theorem 3.7: :(a) Let f be a function from A to B, Inverse relation f -1 is a function from B to A if only if f is one to one ❖ (b) Let f be an everywhere function from A to B, Inverse relation f -1 is an everywhere function from B to A if only if f is one-to-one correspondence. ❖ Proof: (a)(1)If f –1 is a function, then f is one to one ❖ If there exist a1 ,a2A such that f(a1 )=f(a2 )=bB, then a1?=a2 ❖ (2)If f is one to one，then f –1 is a function ❖ f -1 is a function ❖ For bB，If there exist a1 ,a2A such that (b,a1 )f -1 and (b,a2 ) f -1 ,then a1?=a2