Match each schema with the corresponding rule from predicate...

Match each schema with the corresponding rule from predicate logic to prove it, or indicate why it is not a theorem p ? (?x)(p ? x = y) ((?x)?xz) ? x = y ? (?y)x = y (?x)(hgx = y ? T) ? hgx = y ? T *Note there are more options to choose from than needed, and you can use any option as many times as you wish (or not at all) None strong generalization weak generalization specialization

3. What is the truth value of each of the following wffs in the interpretation where the domain consists of integers? a. (∀x)(∃y)(x + y = x) e. (∀x)(∀y)(x < y ∨ y < x) b. (∃y)(∀x)(x + y = x) f. (∀x)[x < 0 → (∃y)(y > 0 ∧ x + y = 0)] c. (∀x)(∃y)(x + y = 0) g. (∃x)(∃y)(x^2 = y) d. (∃y)(∀x)(x + y = 0) h. (∀x)(x^2 > 0) 4. What is the truth value of each of the following wffs in the interpretation where the domain consists of real numbers? a. (∀x)(∃y)(x = y^2) c. (∃x)(∀y)(x = y^2) b. (∀x)(∀y)(x = y^2) d. (∃x)(∃y)(x = y^2) 5. Give the truth value of each of the following wffs in the interpretation where the domain consists of the states of the United States, Q(x, y) is "x is north of y," P(x) is "x starts with the letter M," and a is "Massachusetts." a. (∀x)P(x) b. (∀x)(∀y)(∀z)[Q(x, y) ∧ Q(y, z) → Q(x, z)] c. (∃y)(∃x)Q(y, x) d. (∀x)(∃y)[P(y) ∧ Q(x, y)] e. (∃y)Q(a, y) f. (∃x)[P(x) ∧ Q(x, a)]

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