5. part a.b.c.d For each wff, find an interpretation in which it is true and one

Question

5. part a.b.c.d

For each wff, find an interpretation in which it is true and one in which it is false. a. (Forall x)([A(x) B(x)] [A(x) B(x)]]) (Forall x)(Forall y)[P(x, y) rightarrow P(y, x)] c. (Forall x)[P(x) rightarrow (exist y)Q(x, y)] d. (exist x)[A(x) (Forall y)B(x, y)] e. [(Forall x)A(x) rightarrow (Forall x)B(x)] rightarrow (Forall x)[A(x) rightarrow B(x)] Identify the scope of each of the quantifiers in the following wffs and indicate any variables. a. (Forall x)[P(x) rightarrow Q(y)] b. (exis x)[A(x) (Forall y)B(y)] c. (exist x)[(Forall y)P(x, y) Q(x, y)] d. (exist x)(exist y)[A(x, y) B(y, z) rightarrow

Explanation / Answer

5)

////////a)

Domain = all dinosaurs

True: A(x) = dinosaur had two legs

B(x) = dinosaur had four legs

All dinosaurs had two legs or four legs, and no dinosaurs had both four legs and two legs.

False: A(x) = dinosaur eats meat

B(x) = dinosaur eats plants

All dinosaurs ate meat or ate plants, and no dinosaurs ate both meat and plants. (Ornitholestes was believed to be an omnivore.)

/////////c), the predicate Q(x, y) is an example of a binary predicate

for b and c couldnt build the examples

/////////d)

True: The domain is all positive even integers.

A(x) = “x < 3”

B(x,y) = “y / x is a positive integer”

False: The domain is all positive even integers.

A(x) = “x > 3”

B(x,y) = “y / x is a positive integer”

ALL THE BEST DEAR>>>>>>>>>> ...........

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