Rewrite the following statements using predicate logic. You need to designate the predicate and the propositions. For example, the English sentence

Question

Anyone who thinks Discrete Mathematics is fun is either crazy or an instructor

can be rewritten as follows, assuming that the domain of discourse is all people.

∀x ThinksFun(x, “Discrete Mathematics”) → (Crazy(x) ∨ Instructor(x))

(a) No even number except 2 is divisible by 2

(b) Every discrete mathematics student has to solve homework and some students have to work extra hard

Their sentences are given. And, the three sentences are converted to their equivalent predicate logic forms.

Predicate logic expresses a sentence using some quantifiers like ∀ (for all), ∃ (there exists), etc.

a) No even number except 2 is divisible by 2

¬ ∀x((E(x) ∧ ¬2) → D(x, 2))

where x is a number,

E represents Even

E(x) represents x is even.

D represents Divisibility.

D(x, 2) represents x is divisible by 2.

b) Every discrete mathematics student has to solve homework and some student have to work extra hard

∀x(DMS(x) → (Solve (x, Homework) ∧ (WH(x) ∨ ¬WH(x))

Where x represents student

DMS represents the discrete mathematics student

WH represents work hard

DMS(x) represents ‘x’ is a discrete mathematics student

Solve(x, Homework) represents, ‘x’ solves homework.

WH(x) represents, ‘x’ works hard.

c) It is difficult to study when it is holidays or a weekend

∀x((Holiday(x) ∨ Weekend(x)) → (Difficult (Study, x))

Where x represents a day

Holiday(x) represents ‘x’ is a holiday

Weekend(x) represents ‘x’ is weekend

Difficult(Study, x) represents difficulty to study on the day ‘x’.

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