Recall building a TM M′ where its language or its behavior is based on whether a TM M accepts input string w. For example, consider the following TM M′:
M′ = "On input x :
1. If x ≠ w, reject
2. If x = w , run M on input w and accept if M does."
From the above description, L ( M ′ ) = { w } if M accepts w . Otherwise, L(M′) = ∅. Construct the TM M′ for each specification where Σ ={ 0 , 1 } :
(a) L(M′) = Σ* if M accepts w . Otherwise, L(M′) = ∅.
(b) L(M′) = { x | x ends with a 1 } if M accepts w. Otherwise, L(M′) = ∅.
(c) L(M′) = Σ* if M accepts w. Otherwise, L(M′) ={ x | x ends with a 1}.
(d) M′ accepts exactly two string if M accepts w. Otherwise, M′ accepts more than two strings or less than two strings.