Let f: N to N be defined by
`f(n) = { (((n+1)/2)if n is odd), (n/2 if n is even) :}` for all `n in N`
State whether the function f is bijective. Justify yur answer.

If f: N rarr Z is defined by f(n) ={{:((n-1)/(2),"when n is odd"),(-n/2,"when n is even"):} then identify the type of function

Show that f : N rarr N given by f(x) = { ((x +1), if x is odd), ((x - 1), if x is even) :} is both one-one and onto.

Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 if n is even. Show that f is invertible. Find the inverse of f. Here W is the set of all whole numbers.

Let be a function defined by f(x) =sqrtx is a function if it defined from f : N to N

Let P(n) : n(n+1)(n+2) is divisible by 6. Determine whether the statement is true or false, when n=3 and n=5. Justify your answer.

Let R be a relation from N to N defined by R = {(a,b) in N and a = b^2} . Are the following true? (a,b) in R, (b,c) in R implies (a,c) in R . Justify your answer .

Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true for all natural numbers? Justify your answer.

Let R be a relation from N to N defined by R = {(a,b) in N and a = b^2} . Are the following true? {(a,a) in R , for all a in N }

Let A = {9,10,11,12,13} and let f : A rarr N be defined by f (n) = the highest prime factor of n. find the range of f.

Let N rarr R be a function defined as f(x) = 4x^2 + 12x +15 Show that f : N rarr S , where, S is the range of f, is invertible. Find the inverse of f.