say whether the indicated function is onetoone and what its

say whether the indicated function is one-to-one and what its range is.

(Here A is the set of all finite sets of primes and B is the set N {0}.) Let g : A B, where g(S) is the product of the elements of S. (The product of the elements of the empty set is 1.)

I found out the answer but I still need clearly explanation of this question :(

Solution

In set B 1is an element but none of the products of primes is one hence 1 is not an element in range

as the elements are well defined there is no repitition in set A hence the products are different so each element in A maps single element in B

there fore it is one-one relation

2.

In set B 1is an element but none of the products of primes is one hence 1 is not an element in range

4,8,16...........(powers of 2)

9,27,81,.......(powers of 3)

...........

..............

...................... in B has no mapping from elements in A

hence range is {2,3,5,6,7,10,11,13,15,17,19,..............}

simply we can write as range={x/x=2^^a1.3^^a2.5^^a3.............. k^^ah where a1,a2,a3........ ah are either 0 or 1 and k is the atmost pime in set A}