Sets and Relations - Singapore Maths Olympiad

Suppose that a function M(n), where n is a +ve integer, is defined by
M(n) = n - 10 for n > 100
M(n) = M(M(n +11) for n ≤ 100
How many solutions does the equation M(n) = 91 have?

function

If f(x) = 1 – 1/x, then f(f(1/x)) = ....................

sets and relations

sets and relation

If A = {(n⁴ + 4 n² + 5)/n, n Ɛ Z}, then the number of elements of A are ..........

Sets and relation

If the sets A and B are such that

A = {n Ɛ N; 1≤ n ≤40 and 3 divides n}

B = {n Ɛ N; 1≤ n ≤35 and 6 divides n}

Then the number of elements of A-B are -------