Two Rectangles intersection

Question

I have two rectangles characterized by 4 values each :

Left position X, top position Y, width W and height H:

Answer 1

If the rectangles' coordinates of the lower left corner and upper right corner are :
(r1x1, r1y1), (r1x2, r1y2) for rect1 and
(r2x1, r2y1), (r2x2, r2y2) for rect2
(Python like code below)

    intersect = False
    for x in [r1x1, r1x2]:
        if (r2x1<=x<=r2x2):
            for y in [r1y1, r1y2]:
                if (r2y1<=y<=r2y2):
                    intersect = True
                    return intersect
                else:
                    for Y in [r2y1, r2y2]:
                        if (r1y1<=Y<=r1y2):
                            intersect = True
                            return intersect
        else:  
            for X in [r2x1, r2x2]:
                if (r1x1<=X<=r1x2):
                    for y in [r2y1, r2y2]:
                        if (r1y1<=y<=r1y2):
                            intersect = True
                            return intersect
                        else:
                            for Y in [r1y1, r1y2]:
                                if (r2y1<=Y<=r2y2):
                                    intersect = True
                                    return intersect
    return intersect