If `A={1,2,3,4}`. Prove that `f` defined by `f={(x,y) , x+y=5}` is function from `A` to `A`

Consider set A = {x_(1), x_(2), x_(3), x_(4), x_(5)} and set B = {y_(1), y_(2), y_(3)} . Function f is defined from A to B. Number of function from A to B such that f(x_(1)) = y_(1) and f(x_(2)) != y_(2) is

Consider set A = {x_(1), x_(2), x_(3), x_(4), x_(5)} and set B = {y_(1), y_(2), y_(3)} . Function f is defined from A to B. Number of function from A to B such that f(x_(1)) = y_(1) and f(x_(2)) != y_(2) is

If A = {1, 2, 3, 4} and B= {1, 2, 3, 4, 5, 6} are two sets and function F: A to B is defined by f(x) = x+2, AA x in A , then prove that the function is one-one and into.

If A={1,2,3,4}" and "B={1,2,3,4,5,6} are two sets and function f: A to B is defined by f(x)=x+2,AA x in A , then the function f is

Let f:Xrarr Y be a function defined by f(x)=sinx .

Prove that the function f: N->N , defined by f(x)=x^2+x+1 is one-one but not onto.

Prove that the function f: N->N , defined by f(x)=x^2+x+1 is one-one but not onto.

Prove that the function F : NtoN , defined by f(x)=x^2+x+1 is one-one but not onto.

Let A={x_1,x_2,x_3,x_4,x_5},B={y_1,y_2,y_3,y_4} , Function f is defined from A to B. Such that f(x_1)=y_1 , and f(x_2)=y_2 then, number of onto functions from A to B is (A) 12 (B) 6 (C) 18 (D) 27

Prove that the function f:N to N , defined by f(x)=x^(2)+x+1 is one-one but not onto.