L = { : s ∈ L(M) and |L(M)| % 2 = 0}. For example, suppose that L(M) = {aa}. Then ∉ L because |L(M)| = 1, 1 % 2 = 1; If L(M) {a,aaa} then ∉ L because ℇ ∉ L(M), but ∈ L. Prove that L ∉ D by reduction from H. Your proof could implement R, the mapping reduction function, as a Java or Python program in the form demonstrated, which allows the user to configure whether M halts on w. We start the proof by creating R. We start are by thinking of the input to ouput. What's the input to the function R? Remember that R is a mapping reduction from H to L. So the input to R must be something that could be in H. has the correct syntactic form. Could R return this: ? think of terms of whether the output of R could possible be in L. R() = 1. Define M#: 1.a 1.x Run M on w 2. Return M#,aaa> M halts on w, is in L. So if you make it through step 1.x, then M#,aaa satisfies the characteristic function of L. and if M does not halt on w, is not in L. If you don't get through 1.x, then you lack some component of the characteristic function. attachment Lab9.docx attachment Reduction_Raw_Lecture_notes.pdf attachment Reduction_highlights.pptx