`a-=b` (mod n) and ` b-=a` (mod n) are equivalent

a-=b (mod n) and b-=c (mod n) implies a -= c (mod n)

If a equiv b (mod n), then a^3 equiv b^3 (mod n) (write true or false).

44 ≡ 6 (mod n) where n can be

Let Z Z be the set of all integers and let m be an arbitrary but fixed positive integer. Show that the relation "congruence modulo m" on Z Z defined by : a -= b '(mod m)' implies (a-b) is divisible by m, for all a,b in Z Z is an equivalence relation on Z Z .

If a_(n) and b_(n) are positive integers and a_(n)+sqrt2b_(n)=(2+sqrt2)^(n) , then lim_(nrarroo) ((a_(n))/(b_(n))) =

If a≡b (mod n), then state whether a^2≡b^2 (mod n)

An operation ** is defined on the set A={1,2,3,4} as follows: a**b,ab(mod5) for all a,binA .Prepare the compositon table for ** on A and from the table show that - (i) multiplication mod(5) is a binary operation, (ii) ** is commutative on A, (iii) is the identity element for multiplication mod(5) on A, and. (iv) every element of A is invertible.

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

An operation '*' is defined on a set A={1,2,3,4} as follows: a*b=ab(mod5), all a,b in A ,Prepare the composition table for '*' on A and from the table show that, '*' is a binary opration and '*' is commutative on A.

Let N N be the set of natural numbers and R be a relation on N NxxN N defined by, (a,b) R (c,d) to a+d=b+c, for all (a,b) and (c,d) iN N NxxN N . prove that R is an equivalence relation on N NxxN N .