`2^n gt n` , n is a natural number.

If underset(n)(I) is an identity matrix of order n, then k being a natural number, write the matrix underset(n)(I)overset(k) .

Solve as directed: 2x + 3 gt 15 in integers, in natural numbers.

Let R be a relation in the set of natural numbers N defined by xRy if and only if x+y=18 . Is R an equivalence relation?

If R = {(x, y): x + 2y = 8) is a relation on a set of natural numbers (N), then write the domain, range and codomain of R.

The set N of positive natural number set is finite set or infinite set ?

If N denotes the set of all natural numbers and R be the relation on N xx N defined by (a, b) R (c, d) if ad(b+ c)=bc(a+d) . Show that R is an equivalence relation.

Let R be a relation defined on the set of natural numbers N as follows: R = {(x,y): x in N,y in N and 2x + y = 24). Then, find the domain and range of the relation R. Also, find whether R is an equivalence relation or not.

7^(2n) + 2^(3n-3) 3^(n-1) is divisible by 25 for any natural number n gt 1 .

5^(2(n-4) -6n + 32 is divisible by 9 for every natural number n ge 5 .