Fsc Part 1 Mathematics (Complete Solution)

Q7
Show that the set consisting of elements of the form...

Show that the set consisting of elements of the form a+  3 b(a,b being rational), is an abelian group w.r.t addition.

SOLUTION:

Let G={a+  3 b l, a,b ∈Q}

Let x,y,z∈G a ny three elements of G such that

x=a+  3 b                       , y=c+  3 d        ,            z=f+  3 f

{a,b,c,d,e,f,∈}

(i) x+y=u [U∈Q]  Closure property holds.

(ii) (x+y)+z=x+(y+z)      Associative property holds.

(iii) hence 0=0+  3  x (0)=0∈Q it shows that the additive identity is in 'G'.

(iv) Since x=a+  3 b ∈G,then

-x=-a-  3 b ∈G

Therefore, inverse of each element of ''G'' is also is ''G''

Other Topics

;