Use rules of inference to show that if ∀x(Y(x) → (Q(x) ∧ S(x))) and ∀x(Y(x) ∧ R(x)) are true, then ∀x(R(x) ∧ S(x)) is true.

Q: Solve one of the roots of 6x^2 - 5x = 6 - 5i. Express your answer in rectangular form in 4 decimal p...

A: We have to use quadratic formula  Roots of  ax2+bx+c=0                x=-b±b2-4ac2a Also we have to ...

Q: Evaluate cot-(1 – i) C. 0.3329 + 0.6014i D. 0.4287 + 0.2501i A. 0.7189 + 0.1128i B. 0.5536 + 0.4024i

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Q: Show that [~q a (p → q)] →►p is tautology by constructing truth table.

A:   We know that A tautology is a compound statement in Maths which always results in Truth value. and...

Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. -2 B = , [x]...

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Q: Compute the mark-up price of instant noodles using the given data VCU/U = 20.00 FC = 500.00 US = ...

A: Mark up cost is given by the equation ; Markup cost=unit price·(1+mark up%100)

Q: 404 students were surveyed about their preferences of sports. 126 students like football, 131 studen...

A: Solution

Q: If ax2 +2hxy+by2 =0 represents two straight lines such that the slope of one line is twice of the ot...

A: It is given that the slope of one line is twice the slope of the other line. Let m be the slope of t...

Q: A. Each week, Gavriel buys cheese (C) and sausage (S) which provides her a utility of U- 5th root of...

A: We will use  method of lagranges multiplier . To maximize f(x,y) subject to g(x,y)=k  Solve system o...

Q: Prove: “A graph G is a tree if and only if every two vertices of G are connected by a unique path." ...

A: Let G is the tree. If part: We have to prove, "if G is tree then every two vertices of G connected b...

Q: ) Find the approximate solution x(0.8) using Euler's method for solving dy initial value problem - 4...

A: Given  y ′= 4cos(x + 2y)    with y(0) = 2, h = 0.2

Q: A runner's journal shows the number of miles run each day for a week: Sunday: 3 miles Monday: 5 mile...

A: A sequence is a set of numbers that has a particular order or obeys a general form. In this problem,...

Q: Determine whether there is a Hamilton path on the following graphs. If there is any, draw the path. ...

A: To determine whether there is a Hamilton path on the graphs given. Note that a Hamiltonian path is a...

Q: M Phove that (A nB) <Ã UB

A: Introduction:  A set is nothing but a collection of objects. All the objects must be well-defined. A...

Q: Two airplanes, at points A and B, have elevations of 23,000 feet and 18,000 feet, respectively. Both...

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Q: Use an inverse matrix to find [x]g for the given x and B. 8 B = 5 3 X= 2 - 5 [x]g

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Q: 3 Estimate the minimum number of subintervals to approximate the value of| (4t° + 9t) dt with an err...

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Q: [2 -2 Determine the eigenvalues of the matrix 1 11 3 1 -1 А. —1,2, 3 В. 1, 2, — 3 3 С.- 1, 2, —3 D. ...

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Q: Find the radius of convergence of the power series n· 4n n=1

A: Given series is ∑n=1∞x2nn·4n 

Q: Q7 Let A = [(p → q) ^(~p → ~q)]. Construct a truth table for A and determine if it is a tautology, c...

A: p q [(p→q)∧(~p↔~q)] 0 0 1 0 1 0 1 0 0 1 1 1 [(p→q)∧(~p↔~q)]p⇒q=q∨~p~p⇔~q=(p∧q)∨(~p∧~q)(~p...

Q: 5) – (s + 1)2

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Q: 5. Find the level of each vertex and the height of the rooted tree shown below.

A: The height of a tree is defined as the height of its root node. Note that a simple path is a path wi...

Q: 398 wit

A: In this question, the concept of Simple Interest is applied. Simple Interest Simple interest is comp...

Q: The graph shows a region of feasible solutions. Use this region to find maximum and minimum values o...

A: Given a graph which shows a region of feasible  solutions. We have to find maximum and minimum value...

Q: Solve the following s OWI -D1 1 2 5 f 3 %3D

A: Given that e2-f5=1f-e3=8

Q: (b) Show that 1 11 2 k(k + 2)(k + 4) 96 k=1

A: Given series is ∑k=1∞1kk+2k+4

Q: Evaluate SSS 5el=²+g²+z?)*² dV over B where B = {(r, Y, z) : z² + y² + z² < 1}. Take 7 = 3. %3D

A: A triple integral involves the integral with respect to the product of the variables x,y, and z. In ...

Q: Use a truth table to determine if the following symbolic form of an argument is valid or invalid. -p...

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Q: Find X in base 6= {(40.5)base 8 + (32)base 10} / (A)base16

A: This is a problem of counting, finite math.

Q: 2. For a given function f(x) – (x – 2)² + 6 a) Axis of symmetry : x= b) The vertex (h,k) is: ( c) Ma...

A: The  x co-ordinate of the vertex lies on the axis of symmetry which is situated at the midpoint of t...

Q: (x - 2)" (2n – 1)(2n) Find the interval of convergence of the series - n=1

A: The set of all x-values at which the power series converges is called the interval of convergence. T...

Q: 5. Let V be a vector space over a field F, and let U be a subspace of V. Using the fact that U is a ...

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Q: How many ways can you choose 2 letters from the letters A T C ? Select one: 1 O 720 3

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Q: In the complex number 3 + 4i, the absolute value is: А. 3 В. 4 С.5 D. 6

A: Solution

Q: Consider the function h : N → N given by h(n) = n + (-1)*+l.

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Q: Find the round-off error of the following using 5 significant digits: 1 1. 3 2. tan 150 3. 1 — п 4. ...

A: We can solve this using round off error method According to Bartleby rule i can solve only 1st quest...

Q: Find the Inverse Laplace Transform of the following: 1. F(s) (s+5)6

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Q: I. For z1 = 3 – j5 and z2 = -2 + find the rectangular form of the following: j. Im[- k. j23 I. j23

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Q: If X is normal random variable with mean 3 and variance 5, then find the probability P(2 < X <6).

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Q: Solve : 33x+5 = 92а+8 Ох— 21 O x = — 13 O x = –3 Ог3 —21 Ог— — 11 -

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Q: Find: Sdx. 6e* ex-1

A: Introduction: The process of determining the area of the region under the curve is known as integrat...

Q: 2. For a given function f(x) -(x – 2)2 + 6 a) Axis of symmetry : x= b) The vertex (h,k) is: c) Maxim...

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Q: Question 5. Prove that O- subgroup of itself. (the set of positive rational numbers) under multiplic...

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Q: 2. Use the Newton-Raphson iteration method to estimate the root of the following function employing ...

A: Given fx=xx2-x-10-8=0 and initial guess x0=3.75

Q: 5. For n E N, let fn:X → R such that o # X c R. If each fn is continuous on X but f:X → R is not, th...

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Q: If P(x) = - 0.01x3 +4x2 +70x-1000 is the profit function for a product. Find the rate of change of t...

A: Introduction: The formula for the marginal profit function of the profit function is given by, m(x)=...

Q: R. S3 H.S X1 X2 X3 S1 S2 -4 -3 12 2 0. 4 3. 9. 4 1 4 A simplex Tableau for a linear programming mode...

A: If the objective function is of maximization type. Then in the update table the value of the objecti...

Q: B. Find all spanning trees of the following graph.

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Q: Discuss the equivalences that exist among a given conditional statement, its converse, its inverse, ...

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Q: Question 1. Suppose that G = xy = yx². {e, x, x², y, yx, yx²} is a non-Abelian group with |æ| = 3 an...

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Q: ifth term and twice the third of an arithmetic progression equals the twelfth term. if the seventh t...

A: Introduction: Arithmetic progression is a progression in which each term following the first is obta...