Please help me with Exercice 3.12 Molepo/Desktop/UNISA/MAT2611%20(Linear%20Algebra%2011)/101_2022_0_b(2).pdfG Page viewA Read aloudA Add text- DrawF Highlic1.:RR defined by f(2) = 4x - 15.2. g: R+Rdefined by f(r) = 152.Prove that both f and g are one-to-one correspondences.Let f: A B be a one-to-one correspondence. Then to each be B there corresponds a uniquea E A such that f(a) = b. We define f-1: B A by6) = the unique a such that f(a) = b.Exercise 3.12. Let fA B be a one-to-one correspondence.1. Prove that f-1 is a function.2. Prove that f-1 is one-to-one.3. Prove that -1 is onto.4. Conchide that f1: B→ A is a one-to-ond correspondence.Exercise 3.13. Let f: A B be a one-to-one correspondence. By Exercise 3.12, B A isalso a one-to-one correspondence.1. Prove that fof =i4.2. Prove that o = iB.Set equivalence3.6We are finally in a position to give a formnal definition of the size of a set and to compare differentsizes of sets. Informally speaking, if f : A B is a one-to-one function, then since differentelements of A are mapped to different clements of B, the size of B is at lcast as large as the size ofA. On the other hand if f is onto then since each element in B has at least one element in A thatis mapped to it, the size of B is no greater than the size of A. Thus, one-to-one correspondencesprovide as with a means to compare the sizes of sets. This key observation of Cantor led him to thenotion of two sets being equivalear. Let us read how Cantor defines that two sets are equivalent.We say that two aggregates V and Nare requiva lent." in signs

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Please help me with Exercice 3.12 Molepo/Desktop/UNISA/MAT2611%20(Linear%20Algebra%2011)/101_2022_0_b(2).pdfG Page viewA Read aloudA Add text- DrawF Highlic1.:RR defined by f(2) = 4x - 15.2. g: R+Rdefined by f(r) = 152.Prove that both f and g are one-to-one correspondences.Let f: A B be a one-to-one correspondence. Then to each be B there corresponds a uniquea E A such that f(a) = b. We define f-1: B A by6) = the unique a such that f(a) = b.Exercise 3.12. Let fA B be a one-to-one correspondence.1. Prove that f-1 is a function.2. Prove that f-1 is one-to-one.3. Prove that -1 is onto.4. Conchide that f1: B→ A is a one-to-ond correspondence.Exercise 3.13. Let f: A B be a one-to-one correspondence. By Exercise 3.12, B A isalso a one-to-one correspondence.1. Prove that fof =i4.2. Prove that o = iB.Set equivalence3.6We are finally in a position to give a formnal definition of the size of a set and to compare differentsizes of sets. Informally speaking, if f : A B is a one-to-one function, then since differentelements of A are mapped to different clements of B, the size of B is at lcast as large as the size ofA. On the other hand if f is onto then since each element in B has at least one element in A thatis mapped to it, the size of B is no greater than the size of A. Thus, one-to-one correspondencesprovide as with a means to compare the sizes of sets. This key observation of Cantor led him to thenotion of two sets being equivalear. Let us read how Cantor defines that two sets are equivalent.We say that two aggregates V and Nare requiva lent.&#34; in signs

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Exercise 3.12. Let A B be a one-to-one correspondence. 1. Prove that l is a function. 2. Prove that f- is one-to-one. 3. Prove that - is onto. 4. Conclude that fl: B A is a one-to-one correspondence.