Answer to Question #262186 in Discrete Mathematics for abhi

Question

    Consider the following predicates over the domain of all dogs:

B(x): x barks

W(x): x wags its tail

S(x): x scratches the furniture

T(x): x wants a treat.

H(x): x goes to heaven

Translate the following propositions from simple English to logic or vice versa:

a)     For every dog, if it scratches the furniture, then it does not wag its tail

b)    There exists a dog that does not wag its tail but barks.

c)     ∀x W (x) ∨ ∃x(B(x) ∧ ¬S(x))

d)    ∃x (W (x) ↔ B(x))

e) There exists a dog that does not like treats or scratches on the furniture

f)  All dogs go to heaven, provided they wag their tail and bark.