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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. Youcan only use the given/allowed predicates, along with arithmetic operations (e.g. 2,2) . 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 if 1, then >0 Allowed predicates: G(a, b) a >b, Eqla, 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 cis 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 reciprocal (Reminder: the reciprocal of a real number a is a real number b such that ab 1.) Allowed predicates: Eq(a,b)-a = b The universe (domain) is the set of all real numbers. (d) Statement: There is a real number x, such that for all real numbers y, 2x+y 5. Allowed predicates: Eq(a, b)ab The universe (domain) is the set of all real numbers

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