Let A={{1,2},[1,3},{2},{2,5},{3,4,5}}. Define f: A?N by f(a)=the sum of the elem

Question

Let A={{1,2},[1,3},{2},{2,5},{3,4,5}}. Define f: A?N by
f(a)=the sum of the elements of a (a A)
Find f[A].
Now define g: N?N by
g(n)= { the largest prime = n if n > 1
1 if n=1
Find g ? f and identify its range. Is g one-one? Is g ? f one-one?

Explanation / Answer

Let A={{1,2},[1,3},{2},{2,5},{3,4,5}}. Define f: A?N by f(a)=the sum of the elements of a (a A) Find f[A]. Now define g: N?N by g(n)= { the largest prime = n if n > 1 1 if n=1 Find g ? f and identify its range. Is g one-one? Is g ? f one-one? F[A]...... LET US DESIGNATE THE DIFFERENT ELEMENTS OF SET A AS FOLLOWS.. A1=(1,2)....F[A1]=1+2=3=N1 A2=(1,3)......F[A2]=1+3=4=N2 A3=(2)........F[A3]=2=N3 A4=(2,5).......F[A4]=2+5=7=N4 A5=(3,4,5).....F[A5]=3+4+5=12=N5 HENCE F[A]=N={N1,N2,N3,N4,N5}={3,4,2,7,12}................ANSWER HENCE g: N?N by g(n)= { the largest prime = n if n > 1 1 if n=1 SO WE GET G[N1]=G[3]=LARGEST PRIME

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