Let `NN` be the set of natural numbers and `a in NN`. If `aNN={ax:x in NN} and pNNcap q NN=rNN,` where `p,q,rinNN,` then show that r is the LCM of p and q.

If NN be the set of nature numbers and N_(a) ={an , n in NN}, then N_(5) nnN_(7) is-

If aNN={ax:x inNN} , describe 3NN cap7 NN where NN is the set of natural numbers.

Let NN be the set of natural numbers and A = {3^n-2n-1:n in NN},B={4(n-1):n in NN} . Prove that A subB .

If aNN={ax:x inNN}" then "3NN cap7NN= 3 PNN what will be the value of P ?

Let NN be the set of natural number and f: NN -{1} rarr NN be defined by: f(n) = the highest prime factror of n . Show that f is a many -one into mapping

let NN be the set of natural numbers and f: NN uu {0} rarr NN uu [0] be definedby : f(n)={(n+1 " when n is even" ),(n-1" when n is odd " ):} Show that ,f is a bijective mapping . Also that f^(-1)=f

Let NN be the set of natural numbers and D be the set of odd natural numbers. Then show that the mapping f:NN rarr D , defined by f(x)=2x-1, for all x in NN is a surjection.

Let NN be the set of all natural numbers and R be the relation on NNxxNN defined by : (a,b) R (c,d) rArr ad(b+c)=bc(a+d) Check wheather R is an equivalance relation on NNxxNN .

A relation R is defined on the set of natural numbers NN as follows : (x,y)in R rArr y is divisible by x, for all x, y in NN . Show that, R is reflexive and transitive but not symmetric on NN .

Let NN be the set of natural numbers: show that the mapping f NN rarr NN given by, f(x)={(((x)+1)/(2) "when x is odd" ),((x)/(2)" when x is even"):} is many -one onto.