Problem ( Proving properties of functions) Let A, B be two sets Let f be a function from A to B and let g be a function from B to A For each of the following functions F1,F2, F3 determine whether the stated property is true or false Justify your answer, hence, if the property is true then prove it, otherwise, disprove it 1 The property F1 is bijective, where F1 is given by F1 BA AB(y,x)(x,y) If F1 is bijective, then define F1 1 2 The property if f and g are bijective then F2 is bijective, where F2 is given by F2 A AxHf 1(9 1(x)) 3 The property if f and g are injective then F3 is bijective, where F3 is given by F3 AxB f(A) g(B)(x,y)(f(x),g(y)) Problem ( Proving properties of functions) Let A, B be two sets Let f be a function from A to B and let g be a function from B to A For each of the following functions F1,F2, F3 determine whether the stated property is true or false Justify your answer, hence, if the property is true then prove it, otherwise, disprove it 1 The property F1 is bijective, where F1 is given by F1 BA AB(y,x)(x,y) If F1 is bijective, then define F1 1 2 The property if f and g are bijective then F2 is bijective, where F2 is given by F2 A AxHf 1(9 1(x)) 3 The property if f and g are injective then F3 is bijective, where F3 is given by F3 AxB f(A) g(B)(x,y)(f(x),g(y))

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Problem ( Proving properties of functions) Let A, B be two sets  Let f be a function from A to B and let g be a function from B to A  For each of the following functions F1,F2, F3 determine whether the stated property is true or false  Justify your answer, hence, if the property is true then prove it, otherwise, disprove it  1  The property  F1 is bijective, where F1 is given by  F1 BA AB(y,x)(x,y) If F1 is bijective, then define F1 1  2  The property  if f and g are bijective then F2 is bijective, where F2 is given by  F2 A AxHf 1(9 1(x)) 3  The property  if f and g are injective then F3 is bijective, where F3 is given by  F3 AxB f(A) g(B)(x,y)(f(x),g(y)) Problem ( Proving properties of functions) Let A, B be two sets  Let f be a function from A to B and let g be a function from B to A  For each of the following functions F1,F2, F3 determine whether the stated property is true or false  Justify your answer, hence, if the property is true then prove it, otherwise, disprove it  1  The property  F1 is bijective, where F1 is given by  F1 BA AB(y,x)(x,y) If F1 is bijective, then define F1 1  2  The property  if f and g are bijective then F2 is bijective, where F2 is given by  F2 A AxHf 1(9 1(x)) 3  The property  if f and g are injective then F3 is bijective, where F3 is given by  F3 AxB f(A) g(B)(x,y)(f(x),g(y))

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Problem ( Proving properties of functions) Let A, B be two sets. Let f be a function from A to B and let g be

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