The woman is holding a mug, and has sunglasses on the top of her head.
A woman, who is holding a blue mug, has some red sunglasses on top of her head.
The fact that the woman is holding a mug does not indicate that the mug is blue or any other color.  There is also no way to imply that the color of the sunglasses are red or any other color.
exists e2 e1 x1 x2 x3 x4 x5.(n_head(x5) & of(x5,x4) & n_female(x4) & n_top(x4) & n_woman(x1) & on(e2,x4) & of(x4,x5) & Theme(e2,x3) & Actor(e2,x1) & v_have(e2) & n_sunglass(x3) & Theme(e1,x2) & Actor(e1,x1) & v_hold(e1) & n_mug(x2))
exists e1 e2 s1 s2 x1 x2 x3 x4 x5 x6.(on(e2,x5) & of(x5,x6) & n_head(x6) & of(x6,x1) & n_female(x1) & n_top(x5) & Theme(e2,x4) & Actor(e2,x1) & v_have(e2) & n_sunglass(x4) & a_red(s2) & Theme(s2,x4) & Theme(e1,x3) & Actor(e1,x2) & v_hold(e1) & n_mug(x3) & a_blue(s1) & Theme(s1,x3) & (x1 = x2) & n_woman(x1))