In a family of four A, B, C and D; D is taller than B, C is shortest of all and A is taller than only…

C is shortest and A is taller than only one person, so A is second shortest, and since D is taller than B the order is C less than A less than B less than D. Two people (B and D) are taller than A and two (C and A) are shorter than B, so (i) holds, D is tallest so (ii) holds, and nobody is shorter than C so (iv) holds. A is not shortest and two people are shorter than B, so (iii) and (v) fail.