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Question: 1 let the domain be all the human beings consider...

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1- Let the domain be all the human beings. Consider the following predicates:

D(x) : x is a Democrat

R(x) : x is a Republican

S(x) : x is a senator

H(x) : x is a member of house of representatives

O(x) : x wants to reopen the government

W(x, y) : x wants to work with y

(12 pts) Using the predicates given, appropriate quantifiers, and logical connectives, write each given English language statement as a predicate wff.

(a) Democrat Senators want to work with Republican senators.

(b) Democrat Senators and Republican senators want to reopen the government.

(c) Democrat members of house of representatives do not want to work with Republican senators.

(2) (8 pts) The predicates used here are as defined in the previous problem. Translate each of the following into an equivalent sentence in English. Note: Your English sentences must not involve any variables (such as x, y).

(a) ∀x : O(x) → (D(x) ∧ S(x))

(b) ∃x : D(x) ∧ H(x) ∧ O(x)

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