Answer
a)$P(1,3)\lor P(2,3)\lor P(3,3)$
b)$P(1,1)\land P(1,2)\land P(1,3)$
c)$P(1,3)\lor P(2,3)\lor P(3,3)$
d)$\neg P(1,2)\land \neg P(2,2)\land \neg P(3,2)$
Work Step by Step
a) x can be 1,2 or 3 and there has to exists 1 value out of the three for the propositional function.
$$P(1,3)\lor P(2,3)\lor P(3,3)$$
b) y can be 1,2 or 3 and all values of y are possible.
$$P(1,1)\land P(1,2)\land P(1,3)$$
c) y can be 1,2 or 3 and there has to exists 1 value out of the three for the propositional function.
$$\neg P(2,1)\lor \neg P(2,2)\lor \neg P(2,3)$$
d) x can be 1,2 or 3 and all values have to be possible.
$$\neg P(1,2)\land \neg P(2,2)\land \neg P(3,2)$$
