Let f A B be a function and g: BA be such that g = {(f(a),...

 

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Let f A B be a function and g: BA be such that g = {(f(a), a) a A}. (a) (12 pts.) Write a direct proof in column format of the statement that "if f is onto and one-to-one then g is a function." Your reasons must be drawn from the approved list. Note: h is a function from C to D if and only if for each c C, h(c) is defined/computable, for each c C, h(c) does not produce two different outputs, and for each c C, h(c) D. To prove h is a function you must show it has these 3 properties for the h, C and D that are particular to this problem. Each property requires a separate (short) proof in column format. You should have at minimum 5 steps and maximum 10 over all parts of the proof. (b) (2 pts.) Highlight the first line of your proof from (a) that breaks when f is not onto, and briefly explain why. (c) (2 pts.) Highlight the first line of your proof from (a) that breaks when f is not one-to-one, and briefly explain why. Let f A B be a function and g: BA be such that g = {(f(a), a) a A}. (a) (12 pts.) Write a direct proof in column format of the statement that "if f is onto and one-to-one then g is a function." Your reasons must be drawn from the approved list. Note: h is a function from C to D if and only if for each c C, h(c) is defined/computable, for each c C, h(c) does not produce two different outputs, and for each c C, h(c) D. To prove h is a function you must show it has these 3 properties for the h, C and D that are particular to this problem. Each property requires a separate (short) proof in column format. You should have at minimum 5 steps and maximum 10 over all parts of the proof. (b) (2 pts.) Highlight the first line of your proof from (a) that breaks when f is not onto, and briefly explain why. (c) (2 pts.) Highlight the first line of your proof from (a) that breaks when f is not one-to-one, and briefly explain why.