Showing posts with label propositional logic. Show all posts
Showing posts with label propositional logic. Show all posts

Monday, March 23, 2009

GATE 2002 CS question 1.8 (Propositional logic)

1.8 "If X then Y unless Z" is represented by which of the following formulae in propositional logic?
(a) (X ^ ¬Z) → Y (b) (X^Y)→ ¬Z (c) X → (Y^ ¬Z) (d) (X →Y) ^ ¬Z
Ok, let's first be clear what that statement means: If X then Y unless Z.
In English, A unless B means that A will be true provided B is not true.
So here, the unless means that X being true implies Y also being true, except when Z is true.
So, for Y to be true, we need both X to be true and Z to be false.
This is best expressed by (a) - it literally reads as (X AND NOT(Z)) implies Y.
So, the answer is (a) (X ^ ¬Z) → Y