1. Let p stand for the proposition "I bought a lottery ticket" and q for "I won the jackpot".
Express the following as natural English sentences:
(a) p
(b) pvq
(c) p^q
(d) p q
(e) p⇒-q
(f) -p v (p ^q)
2. Formalise the following in terms of atomic propositions r, b, and w, first making clear
how they correspond to the English text.
3
(a) Berries are ripe along the path, but rabbits have not been seen in the area.
(b) Rabbits have not been seen in the area, and walking on the path is safe, but
berries are ripe along the path.
(c) If berries are ripe along the path, then walking is safe if and only if rabbits have
not been seen in the area.
(d) It is not safe to walk along the path, but rabbits have not been seen in the area
and the berries along the path are ripe.
(e) For walking on the path to be safe, it is necessary but not sufficient that berries
not be ripe along the path and for rabbits not to have been seen in the area.
(f) Walking is not safe on the path whenever rabbits have been seen in the area and
berries are ripe along the path.
Formalise these statements and determine (with truth tables or otherwise) whether