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. Find the truth set for the following predicates: Hint: answer should be a { set }
a) 8/x where x is an integer,the result is in the domain N
b) 8 ≤ p^3 ≤ 125 the result is in the domain Z

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Kenneth G. | Experienced Tutor of Mathematics and StatisticsExperienced Tutor of Mathematics and Sta...
Assuming N is the domain of Natural numbers 0,1,... 
Assuming Z is the domain of Integers ...-2,-1,0,1,2,...
a) 8/x is a natural number when x is positive and x=1,2,4,8.  So the required range set is {8,4,2,1}.
b) 8  ≤ p3  ≤ 125 when p is positive and 2 ≤ p  ≤ 5. The cube of a number is the same sign as the number.
So if p is an integer the required set of values p can have is {2,3,4,5}, and the range is: {8,27,64,125).  If p can be any real number, then the domain is the subset of [2,5] where the cube of the number is an integer, and the range is p3 can be any integer in the range [8,125];