(1) This expression means that both x and y are >0. In that case, the value of the product depends on the value of z.
If z>0, (y+z) can be >0;<0;=0, depending on the value of z vs value of y. As we don't know anything abut z (only z<>0), this is not sufficient.
(2) This expression means that both y and z are >0. In that case, the product will be positive if X>0 and will be negative if x<0. As we only know x<>0, this is not sufficient.
Together, we know x,y and z are >0, so the product is always positive.