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  3. 5 12 points for each part please do the following...

Question: 5 12 points for each part please do the following...

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5. (12 points) For each part, please do the following: . Express each of these statements using quantifiers. You can only use the given/allowed predicates, along with arithmetic operations (e.g. 2,2r). Then form the negation of the statement, so that no negation operator is to the left of a quantifier. . Finally, express this negation you formed in simple and precise English (a) Statement: For all real numbers z, i 2 hen a0. Allowed predicates: G(a, b) = a > b, Eq(a, b) = a = b. The universe (domain) is the set of all real numbers (b) Statement: For all integers a, b, c, if a b is even and b- c is even, then a - c is even Allowed predicate: Eq(a, b)= a=b The universe (domain) is the set of all integers. 3 (c) Statement: There is a real number with no reciproca (Reminder: the reciprocal of a real number a is a real number b such that ab 1.) Allowed predicates: Eq(a, b) ab. The universe (domain) is the set of all real numbers. (d) Statement: There is a real number r, such that for all real numbers y, 2r y 5. Allowed predicates: Eq(a, b)=a=b. The universe (domain) is the set of all real numbers.

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