Question

Let S(x) be the predicate "x is a student in this class", P(y) be the predicate "y completed all levels in Candy Crush" and Q(z) be the predicate "z completed all levels in Angry Birds", where the domain for x, y, and z are all students in the world. Express the following statements by using quantifiers.

Answer 1

(a) A student in this class has completed all levels in Angry Birds and Candy Crush.

(b) All students (of this class) who have completed all levels in Angry Birds have not completed all levels in Candy Crush.

(c) One and only on student of this class has completed all levels in Angry Birds and Candy Crush.

Answer 2

a)\[\exists x \in S(x) \implies \forall (P(y) \wedge Q(z))\]
b)\[\forall x \in S(x) \implies \forall \neg P(y) \wedge Q(z)\]

Answer 3

not sure about last one neither the 2nd one

Answer 4

One and only one student of this class has completed all levels in Angry Birds and Candy Crush.