Write in the language of the predicate logic with proper

Question

1. Write out the formal structure of this deduction, then decide whether it is valid argument giving your reasons why you think it is a valid deduction (from Lewis Carroll):

(a) Nothing intelligible ever puzzles me.

(b) Logic puzzles me.

(c) Therefore, logic is unintelligible.

2. Let the universe be the set of integers, and let G(x, y) be the sentence "x² ≠ y" for x and y variables with values in this domain.

Using this sentence G, write in the language of the predicate logic the sentence: "There is an integer whose square is 25."

3. Let the universe be all animals. Write in the language of the predicate logic with proper quanti?ers and parentheses the statement: "Some cats chase any dog." Let C(x) be "x is a cat, D(x), " x is a dog", and Ch(r,s), "r chases s".

4. (3) Let the universal set be the set R of real numbers, X = {a ∈ R |-7 a< 2} and Y = {a ∈ R |- 4

Find:

a) X ∩ Y

b) X - Y (The set of all a in X but not in Y.

c) The set of all a in X or Y but not in both.

5. Let S(x, y, z) be the sentence: z =(y² ) ∗ x with the domain being the set of integers. Write the sentence for S(x + y, 2z²,x).

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