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.