Deductive Reasoning in First-order Logic 205 (c) Every child is a pedestrian No driver is a pedestrian Johnie is a child Therefore somebody is not a driver (d) All penguins are birds Some penguins are white All penguins eat some fish Therefore, there is a white bird that eats some fish (e) All penguins are birds No penguins can fly All seagulls can fly All fat birds are penguins Some fat birds are white Therefore, there is a fat white bird that is not a seagull (f) No yellow plonks are qlinks Some object is a plonk or not a qlink Therefore, there is an object which is not a yellow qlink (g) Victor is a hungry student Every student either studies or parties Every student who is hungry does not study Therefore, some student parties 4.5.6 Formalize each of the following statements in first-order logic and check whether it logically implies the other If any of the logical consequences not hold, give an appropriate counter-model A: “No man is happy only when he is drunk.” B : “There is a happy man and there is a man who is not drunk.” 4.5.7 Using the predicates: D(x) for “x is a dragon,” E (x) for “x is an elf,” F (x) for “x is a fairy,” F l(x) for “x can fly,” G(x) for “x is a goblin,” H (x) for “x is a hobbit,” T (x) for “x is a troll,” U (x) for “x is ugly,” and L(x, y ) for “x likes y ,” formalize each of the following arguments in first-order logic, in the domain of all “mythic creatures.” Check whether each is logically valid If it is not valid, give an appropriate counter-model