Please help with predicate!!!!

Question

If the domain is  - the set of all integers (i.e.,  ), then the predicate 

   

is TRUE for all of the following values of :

a.) No values of in this domain make the predicate true

b.) - this is the closed interval containing all real numbers between  and  inclusive

c.) x ∈ {2,3,4}

    

Answer 1

We are looking for the set { x in Z | (x-3)² ≤ 1 }, that is, all integers making P(x) true, so all integers x such that (x-3)²≤1. Since we are only considering integers, the only x values that work are x=2,3,4 so we get the answer c). Note that if our domain was all real number instead, then the answer would be b).