यदि लेखनी < पेनसिल, पेनसिल < पुस्तक तथा पुस्तक > टोपी, तो निम्नलिखित में से कौन-सा एक सदैव सत्य है?

Correct Option: Pen < Book

We are given the following relations: (1) Pen < Pencil, (2) Pencil < Book, and (3) Book > Cap (which can be written as Cap < Book). Let us evaluate the options based on these inequalities. From relations (1) and (2), by transitivity, we have: Pen < Pencil < Book. This directly implies Pen < Book. This relation is always mathematically true regardless of the values. On the other hand, the relationship between Pen and Cap, or Pencil and Cap, cannot be definitively determined because we only know that both Pen and Cap are less than Book, and Pencil is less than Book, but we have no relative information comparing Cap with Pen or Pencil. Thus, 'Pen < Book' is the only statement that is always true. Hence, option B is correct.