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

1 comment:

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