Question 3: Suppose that A, B, and C are three sets (possibly infinite). Show that if ƒ: A → B is an injection, and g: B

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Question 3 Suppose That A B And C Are Three Sets Possibly Infinite Show That If F A B Is An Injection And G B 1 (210.92 KiB) Viewed 10 times

Question 3: Suppose that A, B, and C are three sets (possibly infinite). Show that if ƒ: A → B is an injection, and g: B → C is an injection, then go f is an injection from A to C. Note: A consequence of this is that if |A| ≤ |B| and |B| ≤ |C|, then |A| ≤ C. This consequence only becomes interesting when A, B, and C are infinite, since otherwise |A|, |B|, and C are just integers.