Lower Bounds - US

Practice problem 2, Reading 76 Volume 6 Are the solutions for B (US style options) incorrect given that they have discounted the value of the Xprice? My understanding was that the lower bound for US style was zero or instrinsic value only or Call: Max(0,S-X) Put: Max(0,X-S)

Sure it just says that an American option is worth at least it’s intrinsic value. That’s really easy to see because you could just exercise it and pick up the intrinsic value.