Use the PMI to prove the following for all natural numbers:(a) is divisible by 3. (b) is divisible by 3.(c) is divisible by 6.(d) is divisible by 12.(e) 8 divides(f) is divisible by 9.(g) 8 divides(h) (i)(j)(k)(l) For every positive real number x,(m) is an integer.(n) Using the differentiation formulas andprove that for all(o) If a set A has n elements, then has elements.

i,r'"-) '6>"\\ UD )"j inur,Ef*r**r*{, F .",-f< {-rc-t ( it\trL;- i 1-nc-'*r- ''\ iIt_./\--tl.;e,lCl) ' (-- \(,u '-\, lc I J') -1 C - tQg-.[e-& vS\'-r-,"- u:.\\ \\t,C rL*. i-a-V,:t*i: l.\t /", tiirt L I : c, ;c,5\ -Ll (o ,le\t \\ {, l. L*7 -:;-f-*' L: i,\ i) "'P('-)' "- 'K"l to.tt"ot n {^- ; ,ij{-,To,g"'a*