Which statement must be true?

5. If \(a<b<c\) and \(a<d<c\), which of the following statements must be true?

      1. \(a<c\)
      2. \(b=d\)
      3. \(b<d\)


  1. I only
  2. II only
  3. III only
  4. I and II
  5. I, II and III

$$\text{We know that:} \begin{cases} a<b>c\\ a<d<c \end{cases}$$

Which means both b and d lies between a and b as explained in following figure, but we don't know if b is equal to, greater or less than d.

Answer: A