Let's say we're in a proof and we know: (∀d)(S(d)→R(c,d))→(∀d)(M(d)→R(c,d)) Suppose we wanted to do universal instantiation, substituting scrat for the d's bounded by the first (leftmost) occurrence of (∀d). What is the result of this substitution? Group of answer choices (S(scrat)→R(c,scrat))→(∀d)(M(d)→R(c,d)) (S(scrat)→R(c,scrat))→(M(scrat)→R(c,scrat)) S(scrat)→R(c,scrat) (∀d)(S(d)→R(c,d)→(M(d)→R(c,d)))     2. In a proof, which of the following lines "push the stack?" (I.e., add to the number of vertical lines on the left-hand-side?) Group of answer choices Let n be an arbitrary natural number. Since a

The proof in the attached image is given for Bayes theorem, however I am quite a bit confused so if able please explain the proof in more detail step by step, thank you in advance.

7. (a). Find the sum-of-products expansion of F(x, y, z) identities and justifying each step. = x + y + z using only Boolean (b). Find the sum-of-products expansion of F(x, y, z) x by filling the following table. The last column has to yield your answer. Note that you need to expand x(y + y) (z + z) correctly to get the sum-of-products expression in the last column. X Y Z y+yz+zx(y+y)(z+z)| F(x, y, z) = 1 1 1 1 1 0 10 1 1 00 0 1 1 0 1 0 001 000

19. Let f(n) be defined recursively by f(0) = 3, and f(n + 1) = 3f(n)/3, for n = 0, 1, 2, . . . Then, f(10) = _____________.