Is this a true statement Justify your response Let f X right

Is this a true statement? Justify your response. Let f: X rightarrow Y,be a function, and suppose thatand E satisfy (x_0, y_0) e f. If (x,y) E f, and x x_0,then y = y_0

Solution

The statement is true only if f is a one-to one function i.e. if f maps distinct elements of X to distinct elements of Y. Thus, if f is a one to one function and x₀ , x₁ X and y_0, y₁ Y such that f(x₀) = y₀ and f(x) = y and x₀ x, then the statement that y₀ y is true.