Correct Option
The given inequalities are:
- Pen < Pencil
- Pencil < Book
From these two statements, it can be logically deduced that if Pen is smaller than Pencil, and Pencil is smaller than Book, then Pen must necessarily be smaller than Book. This is based on the transitive property of inequalities. Therefore, "Pen < Book" is always true.
Incorrect Options:
Option (1): Pen > Cap
We are given Pen < Book and Book > Cap (which implies Cap < Book). While both Pen and Cap are less than Book, their relationship to each other is not definitively established. Pen could be greater than, less than, or equal to Cap. For example, if Book = 10, Pen could be 5 and Cap could be 3 (Pen > Cap), or Pen could be 3 and Cap could be 5 (Pen < Cap). Thus, this statement is not always true.
Option (3): Pencil = Cap
We know Pencil < Book and Cap < Book. There is no information provided that suggests Pencil and Cap must be equal. They are independent variables, each constrained only by being less than Book. Therefore, this statement is not always true.
Option (4): Pencil > Cap
Similar to Option (1), although Pencil < Book and Cap < Book, these conditions do not guarantee that Pencil is always greater than Cap. Pencil could be greater than, less than, or equal to Cap. For example, if Book = 10, Pencil could be 8 and Cap could be 6 (Pencil > Cap), or Pencil could be 6 and Cap could be 8 (Pencil < Cap). Hence, this statement is not always true.