# Find joint pdf table of two discrete independent random variables $X$ and $Y$

Given the pdfs of two discrete independent variables $$X$$ and $$Y$$, write the joint pdf. There is a property that $$if\ \ p_{XY}(x,y) = p_X(x)p_Y(y) \ \forall i,j \Rightarrow \text{X,Y are independent}$$. I am not that sure if this statement is true for $$"\Leftarrow"$$ and I cannot find another way to solve this problem.