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Additional information: r(x) is the open statement "x>0". The universe is integers.
Given additional information:
r(x): x>0 (open statement, true for all positive integers) p(x): x < 3 (true for x=1, 2 and false for all other integers) q(x): x + 1 is odd (true for odd integers and false for even integers)
Step by step
Solved in 2 steps
- For f (a, b) = (a | b) | b(a) Simplify f (a, b).(b) Find DNF for f (a, b).(c) Is f (a, b) satisfiable?The sequence of values: n, c(n), c(c(n)), c(c(c(n))), c(c(c(c(n)))),... is known as the hailstone sequence starting at n. Implement c(n) as a function. Use predicates to test the parity of each input n.Describe each of the following sets.a. {x ∈ R|−5 < x < 1}b. {x ∈ Z|−5 < x < 1}c. {x ∈ Z−|−5 < x < 1}
- A common way of implementing a max function is to look at the sign of a - b. In this case, we can't use a comparison operator on this sign, but we can use multiplication. Let k equal the sign of a - b such that if a - b >= 0, then k is 1. Else, k 0. Let q be the inverse of k.n implement the code:Let Σn denote the set of all binary strings with lengths less than n. For example, Σ2 = {λ, 0, 1} and Σ3 = {λ, 0, 1, 00, 01, 10, 11} where λ is the empty string, i.e. the string of length 0. For x ∈ Σ we denote the length of x by |x|. a) How many functions f : Σn → Σn are there? b) How many one-to-one functions f : Σn → Σn are there?Q: Compute the longest common subsequence by computing the table for given two strings. X = <T, A, G, T, C, A, C, G> Y = <A, G, A, C, T, G, T, C>
- Write a wff of P that is equivalent to the following wff involving a different quantifier. ¬(∃x)(Wx ∧ Hx)Computer Science Draw the TST that results from inserting the following strings into an initially empty trie now is the time for all good people to come to the aid of(a)Describe a bijection from the set of binary strings of length n to the set of binary strings of length n + 1 which have an even number of 1s.(b) How many binary strings of length n + 1 have an even number of 1s?
- The format P(X) represents as a power set of given "X", (of all X's subsets) Now, assume there are two sets A= {q, w, e, r} and B = {w, r, f}. (a) What are the elements of P(A) ∩P(B )?(b) What is the cardinality of P(A ∪B )?(c) What is |P(A) ∪P(B )|?Show the {(p V q ) ^ not p} implies (q V not q)a)Write a recursive definition for the set of odd positive integers. b)Use master theorem to find the solution to the recurrence relation f(n) = 4f(n/2) + 2? ! ,when n = 2" , where k is a positive integer and f(1) = 1.