A. Falsehood: Truth: A falsehood is a lie, which is the opposite of truth. This is not a similar relationship.
B. Hearsay: Authenticity: Hearsay refers to information received from others that may not be reliable, while authenticity relates to something being genuine or credible. This shows a similar relationship where hearsay lacks authenticity, much like presumption lacks certainty.
C. Theorem: Proof: A theorem is a statement that can be proven, but this implies certainty rather than a lack of it, making it different from the original pair.
D. Hunch: Guess: A hunch is an intuitive feeling or belief without strong evidence, and a guess is an estimate or opinion without sufficient information. While related, this relationship is not as direct as the first pair.The correct option is (B): Hearsay : Authenticity