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C can e be recursive yes let t then e x x

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Unformatted text preview: {f | ∃<x,t> [stp(f,x,t) && value(f,x,t) = 0] } 2/23/14 © UCF EECS 4 Sample Ques+on#5 5. Let S be an re (recursively enumerable), non- recursive set, and T be re, non- empty, possibly recursive set. Let E = { z | z = x + y, where x ∈ S and y ∈ T }. (a) Can E be non re? No as we can let S and T be semi- decided by fS and fT, resp., E is then semi- dec. by fE (z) = ∃<x,y,t> [stp(fS, x, t) && stp(fT, y, t) && (z = value(fS, x, t) *value(fT, y, t)) ] (b) Can E be re non- recursive? Yes, just let T = {0}, then E = S which is known to be re, non- rec. (c) Can E be recursive? Yes, let T = ℵ, then E = { x | x ≥ min (S) } which is a co- finite set and...
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