Given the shortest side of a 30° by 60° by 90° triangle, find out the other two sides. Return the longest side and medium-length side in that order. Examples otherSides (1) [2.0, 1.73] otherSides (12)→ [24.0, 20.0] otherSides (2) [4.0, 3.46] otherSides (3) → [6.0, 5.2]

Q: Computer Science p=317, q=811 (a) Consider the multiplicative group F∗p and find a generator…

A: Here is the explanation:

Q: Prove the argument(∀x)[(B(x) ∨ C(x)) → A(x)] → (∀x)[B(x) → A(x)]

A: Given argument, (∀x)​[(B(x) V C(x)) → A(x)] → (∀x)​[B(x) → A(x)]

Q: For the sample space S = {c,d,e,f,g,k,l}, identify the complement of A = {d,f,k,}.

A: Set theory is a branch of mathematical logic that studies the properties and relationships of sets,…

Q: Write a Scipy program for floyd warshall matrix [0, 1, 2], [1, 0, 0], [2, 0, 0]

A: Here I written Scipy Code for given problem floyd warshall. I hope you like it. Used: Goooglee…

Q: Using tables, find the sum of products of expansions of the following Boolean functions.  F (x, y,…

A: Here in this multiple question we have given two function and we have to find sum of products…

Q: Find the sum of (736)8 + (147)8 with steps.

A: Eight different digits are used to represent numerical values in the octal number system, also known…

Q: Use two different ways to prove XY + Z= (X+Z)(Y+Z). a) Purely Algebraic way p) K-map

A: (X+Z).(Y+Z) =X.(Y+Z) + Z.(Y+Z) =X.Y +X.Z+ Z.Y+ Z =X.Y+Z.(X+Y+1) =X.Z + Z.(X+1)  [Y+1=1] =X.Z + Z

Q: Given: ∀x [p(x) → q(x)] ∀x[p(x) → (∀y w(y))] ∀x ∀y [(q(x) ∧ w(y)) → s(x)] p(MARY) Show s(MARY)…

A: The answer is as follows.

Q: Given a cycle graph C, and a complete graph Kn on n vertices (n2 3), select all the correct…

A: The correct answer along with the explanation.

Q: Simplify the following Boolean functions, using K-maps: F (w, x, y, z)=Σ(11, 12, 13, 14, 15)

A: To simplify the Boolean functions, using K-maps, first we need to draw a Kmap for four variable.…

Q: 4. Let G=(V, E) be the following undirected graph: V = {1, 2, 3, 4, 5, 6, 7, 8} E = {(1, 7) (1, 4),…

A: An undirected graph is a graph, i.e., a set of objects (called vertices or nodes) that are connected…

Q: your work.) Consider the degree-4 LFSR given by P(x) = x² + x² + 1. Assume that the LFSR is…

A: the answer is an 6

Q: Let U = {2,3,4}. Find the power set P(U).

A: Let U = {2,3,4}. Find the power set P(U).

Q: Q6 Minimize the following minterms using K-MAP Ү-D m (1 ,5,6, 7, 11, 12, 13, 15)

A: Objective: The given minterms should be minimized by using K-MAP.  Y=m(1, 5, 6, 7, 11, 12, 13, 15)…

Q: A sample space of five elements E1, E2, E3, E4 and E5. Find P(E4) and P(E5) if: P(E1) = P(E2)=0.15,…

A: The question is to find P(E4) and P(E5) from the given conditions.

Q: (p ∧ q) → (p ∧ ∼r) Construct a truth table

A: TRUTH TABLE for above :   p q r (p ∧ q) → (p ∧ ~r) F F F T F F T T F T F T F T T T T F…

Q: Given a function f(a,b,c,d) = Σm(0, 1, 9, 13, 15), Σd(3, 4, 5, 6, 8), find a simplified function f…

A: a) Sum of Product SOP - Given, f(a,b,c,d) = Σm(0, 1, 9, 13, 15),+Σd(3, 4, 5, 6, 8) Sgiven boolean…

Q: Let D be the 11-ary code of length 10 defined as the linear span of (1,4, 1, 2, 1, 4, 2, 6, 4,0) and…

A: To show that thе codе D is a subcodе of a cyclic codе of dimеnsion 8,  wе nееd to dеmonstratе that D…

Q: Let v be a vector whose coordinates are given as v = [Vx, vy, Vz]". If th %3D quaternion Q…

A:

Q: Write a program to plot the relation of the following functions…

A: Algorithm :  Step 1 : store the interval from 0 to 4pi in a vector with step size pi/50. Step 2 :…

Q: Find a basis for and the dimension of the subspace w of R4. w = {(0, 4t, t, -t): t is a real number}…

A: Given: Sub-space W of R4 is = {( 0, 4t, t , -t ) : t is real numbers}

Q: c,d 00 01 11 10 a,b 00 1 1 1 01 11 10 1 1 1

A: Layout : Groups : d` = (0,2,4,6,8,10,12,14) b`.c` = (0,1,8,9) Expression : F= d` + b`.c`

Q: P(x): x is yellow; the domain of interpretation is the collection of all flowers. P(x): x is a…

A: First one is not true Second is true

Q: Write an FSM that accepts those binary numbers with their number of 1s being multiples of three,…

A: Multiple of 3 means number of 1's can be 0,3,6... The total number of states in the FSM will be 3…

Q: Complete the truth table of the following. ~p˄(p→q) (p→q)˄(q→r) [p˄(~q)]v[(~p)vq]

A: 1) Truth table of the first position: ~p˄(p→q) truth table is given below:

Q: Minimize the following minterms using K-MAP Y= m (0, 1, 2, 5, 13, 15 )

A: Given range 0-15 .  So 4 variable K map will be used.  To find? Minimized boolean function.

Q: The correct statements are: Let R = {(1,2), (2,3), (3,4)}. {(1, 2), (2, 3), (3, 4), (1, 3), (1, 4),…

A: In this question we have to understand about the select the correct from thevgiven statements on the…

Q: Find the power set P(A), of set A, where A ={5,{π,e},7,{5,7}}.

A: Here we have given the power set p(A) for the given set A.

Q: Affine transformations preserve parallel lines. True or false

A: A transformation that preserves lines and parallelism (maps parallel lines to parallel lines) is an…

Q: Find a countermodel for each of the following wffs: 3x p(x) → Vx p(x) Væ (p(x, f(x)) → p(x, y))

A: Counters are an uncommon instance of limited state machines since they move straightly through their…

Q: If n points are connected to fom a closed polygon as shown below, the area of the polygon can be…

A: The algorithm to develop the C program for computing area of the polygon with n sides is as follows:…

Q: 8. Suppose f and g are functions from R → Rwith f(x) = [2] and g(x) = [52]. Find (fog) (5)

A: 1. Programming is the process of creating a set of instructions that tells a computer how to perform…

Q: For S = {1,{1,2},3} find the power set P(S)

A: Given subset is  S= {1,{1,2},3}  Power set is P(S).

Q: How do I create graphs of the function f(x)=2 sin(x-pi/4), for x running from 0 to 2 pi, and x in…

A: Let's start to create graph of the function f(x) = 2 sin (x - π4) , for x running for 0 to 2 pi and…

Q: 3. ( >Watch the video XOR/XNOR Patterns in K-Maps (4:41) and find the logic expressions of these 4…

A: Steps to solve expression using K-map- For SOP put 1’s in blocks of K-map respective to the minterms…

Q: Prove that if 3x(P(x) → Q(x) is true, then VxP(x) → 3xQ(x) is true.

A:

Q: Draw a graph G containing the following vertices and edges. V(G) = {0, 1, 2, 3, 4, 5, 6} E(G) = {…

A: To draw a graph G with the given vertices and edges, we can represent the graph using an adjacency…

Q: Find all strings in L ((a + bb)∗) of length five.

A: Answer:The symbol “+”denoted as “OR” operator which means “a + b” means either “a” or “b”, so the…

Q: Given an n-sided regular polygon n, return the total sum of internal angles (in degrees). Examples…

A: In this question we need to write a C++ program where we need to implement a function which takes no…

Q: -19 Consider the group E23(9, 17). This is the group defined by e equation y2 mod 23 = (x³ + 9x +…

A: Answer: Given a=9,b=17, p=23 y2=x3+9x+17 mod 23  We have to find the what is the value of K

Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.