Let A be a set of cardinality n where n E N Assume m E N and

Let A be a set of cardinality n, where n E N. Assume m E N and m

Solution

Let A be a set of cardinality n where n belongs to N. i.e A={a_1,a_2,a_3,.....a_n} Assume that m belongs to N and m<=n. let B is subset of A and B={b_1,b_2,....b_m} where m belongs to N and by hyp. m<=,n. Now we have function f:A to B f(n)=m, so the map is injective as f(n₁)=f(n₂) is m₁=m₂ is same as n₁=n₂   to prove surjective we can take m belongs to N such that m=f(n)=n so map is surjective. therefore f:A to B is one to one correspondence. Hence, B is finite set with cardinality m.