Consider the set N= {f f is an injective function from a subset of X to...

 

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Consider the set N= {f\ f is an injective function from a subset of X to a subset of Y}. Define an ordered relation < on 2 as follows: for f,g eN, ƒ <gif f C 9, where f C g if for every (x, y) E f, (x, y) E g. Clearly < is an ordered relation on N. a) Show that 2 is not empty. b) Let IC N be a non-empty chain of N. Let h:=Us. Ser i) Show that h is a function from a subset of X to a subset of Y. ii) Show thathen, and it is an upper bound of r. c) Conclude that 2 has a maximal element. 42,5,8,5)| Consider the set N= {f\ f is an injective function from a subset of X to a subset of Y}. Define an ordered relation < on 2 as follows: for f,g eN, ƒ <gif f C 9, where f C g if for every (x, y) E f, (x, y) E g. Clearly < is an ordered relation on N. a) Show that 2 is not empty. b) Let IC N be a non-empty chain of N. Let h:=Us. Ser i) Show that h is a function from a subset of X to a subset of Y. ii) Show thathen, and it is an upper bound of r. c) Conclude that 2 has a maximal element. 42,5,8,5)|

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a Here X and Y are non empty and finite So there exist an x in X and a y in Y Now the relation mappi... View the full answer