Prove the following argument is valid: Væ [p(x) → (q(x) V r(x)] Væ (r(x) → q(x)] -3x q(x) 3x p(x) ..

Q: For a given predicate P(x), you might believe that the statements VxP(x) or 3xP(x) are either true…

A: A Predicate is a revelatory sentence whose valid/bogus worth relies upon at least one factors.  The…

Q: Given that: U={1, 2, 3,..,20} A= {x: x is odd} B = {1,3,4,7,12,15,18} C = {x: x is the multiple of…

A: I ) We have     U = { 1 , 2 , 3 , ........, 20 }   A = { X : X is odd } =  { 1 , 3 , 5 , 7 , 9 , 11…

Q: Write a python code of a function that takes in four points in a counterclockwise order, a, b, c, d…

A: Program Instructions:Create a function isConvex() and pass the four points as arguments.Save the…

Q: we know that P(A) = 1/4, that P(B) = 1/2, ar P(B|A) = 1/2, what is P(A|B) ? and that

A: Solution P(A/B)= 1/4 Conditional probability Probability of A happened given that B is happened…

Q: Give the cardinality of the power set of set B = {{a, b, c}}. %3D 3 O 8 O 2 O 4

A: The cardinality of a set is the number of distinct elements in the set. A power set includes all the…

Q: Show the {(p V q ) ^ not p} implies (q V not q)

A: Logic of implies says that If A is true then B must be true,  if A is not true then B can be…

Q: (a)Describe a bijection from the set of binary strings of length n to the set of binary strings of…

A: Answer:-

Q: Let Σ = {a, b}. Indicate whether or not L is regular and prove your answer.   (i) L={w ∈ {a, b}* :…

A: Regular Expression: A regular expression is exists for all the regular languages. A regular…

Q: 3. Prove that (P =Q) = R has the same truth with (P = R) ^ (Q=R). We write (P=Q)=R= (P=R) ^ (Q=R).

A: Given:   Prove that (P⇒Q) ⇒ R has the same truth with (P⇒ R) ^ (Q⇒R).

Q: log 2 (x +3) x2 +3x + 2 Find the domain of definition of f (x)=

A: Solution :-_

Q: f : {1, 2, 3} ® {a, b, c, d} f(1) = c f(2) = b f(3) = a g : {a, b, c, d} ® {x, y, z} g(a) = y g(b) =…

A: The answer is given below:-

Q: This is a proof by induction over, The property P =

A: This is very simple. The question is based on Propositional Logic   proposition, proposition…

Q: Show that ~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p Show that q→ p ≡ ~ p → ~ q Show that p→q ≡ ~ q → ~ p

A: ~ (p ∨ q) ∨ (~ p ∧ q)  = ~ (p ∨ q) ∨ ~( p ∨ ~q)     [ De morgan's law ] = ~ ((p ∨ q) ∧ ( p ∨ ~q))…

Q: Proof that the following given propositions. 1. (p + r) A (q + r) - (p V q) + r 2. (p + q) v (p + r)…

A: A tautology is a mathematical assertion in which if the given proposition is said to be tautology…

Q: A well-known problem in computer science is called the knapsack problem. A variation is as follows:…

A: int knapsackRec(int[] w, int[] v, int n, int W) { if (n <= 0) { return 0; } else if (w[n - 1]…

Q: Let U={1,2,3,4,5,6,7,8,9}, A={2,4,6,8}, then

A: I Have answered this question in step 2.

Q: Write the sets A and B if A – B = {1, 5, 7, 8}, B – A ={2, 10}, and A NB = %3D .{{3, 6, 9

A: Summary : If a - b = {1, 5, 7, 8}, b - a = {2, 10}, and a ∩ b = {3, 6, 9} then the value of sets a…

Q: For the two chains of number sets given here, derive a rule for moving along an arrow, and a rule…

A: Given two chains are, {57,36}→{21,36}→{21,15}→{6,15}→{6,9}→{6,3}→{3,3}={3} stop…

Q: Find the sets A and B if A – B = {1, 4, 7, 11}, B – A ={2, 20}, and 4 N B= {3, 5 ,19}

A: here is your answer

Q: If five integers are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8}, must there be at least two…

A: Initially, the set X can be partitioned into four subsets: {1, 3}, {2, 4}, {5, 7}, {6, 8}.   We…

Q: Given the sets A = { A, B, C, D} and B = {C, D, E}, what is A  v B  A-B

A: Given sets are: A={A,B,C,D} B={C,D,E} Now , we have to find A U B and A-B.

Q: Find g of (a) f:Z→ N, (b) f:R → (0,1), f(x)=1/(x² +1); f(n) = n² + 1; g:N → Q, g(n) = g: (0, 1) →…

A:

Q: Construct an indirect proof: Q v (R ∙ S) (Q ⊃ T) ∙ (T ⊃ S) ∴ S

A: Indirect proof: There are two methods of indirect proof: proof of the contrapositive and proof by…

Q: Reduce the following Boolean expression using K-Map:- F(U,V,W,Z)= T(0,2,5,7,12,13,15)

A: Here we need to simplify or reduce the given Boolean expression and draw the K map by using the…

Q: Is A a subset of B if; A = { 9, 8, 7, 6, 5}   B ={ 5,6, 7, 8, 9}

A: Overview : A collection of elements is known as a subset if all the elements of the set are…

Q: (a) Show that 3x(Px x Px). (b) Show that {Qx,V y(Qy → Pz)} EX Px.

A: The solution for the above-given question is given below:

Q: n-17 .. n. For example, if n = 4 and k = 2, a solution is: [ [2,4], [3,4], [2,3], [1,2], [1,3],…

A: Machine independent language :- > the language which does not depend on the computer or its parts…

Q: A set of integers are relatively prime to each other if there is no integer greater than 1 that…

A: If n is Prime then φ(n)=n-1 In then Given options Options A and E have n as Prime. So…

Q: Let f (x) = (x +2)(x+1)²x(x - 1) (x – 2). To which zero of f does the Bisection method converge when…

A: Let . Now, Therefore,  are the zero’s of

Q: Prove that x, where y is the domain of all real numbers, if x²(y² - 2y) is odd, then x and y are

A: A function f is termed as odd if the condition f (-x) = -f (x) holds. Whereas a number is odd if it…

Q: Consider the following sets: U = {a,b,c,{a,b},d,{b,c,d},e} A = {a, b,{a,b}, {b,c,d},e} B = {a, b,c,…

A: U = {a, b , c , {a,b} , d , { b, c , d} , e } A = {a, b , {a,b} , { b, c , d} , e} B = { a , b , c ,…

Q: For all sets A, B, and C, it holds that (An C) U (B \ C) = (B U C) \ (C \ A).

A: We can do the set interpretation of LHS and RHS to answer the question.

Q: A well-known problem in computer science is called the knapsack problem. A variation is as follows:…

A: Given: grade 12 computer science chapter Recursion * Returns true if there exists a subset of the…

Q: Order the following functions by asymptotics with respect to Ω. That is, find an ordering f1 , f2 ,…

A: Say, f1 = Ω(n2) = n2 f2 = Ω((2)log(n)) = log(n) f3 = Ω(n!) = n! f4 = Ω(log(n)!) = log(n)! f5 =…

Q: Construct the truth (tables) values of the given compound proposition: [(p^q'Ar) + (p O q)] – [(p' &…

A: XOR is represented by ⊕. AND is represented by ∧. OR is represented by ∨. ↔ represents…

Q: Simplify the following expression to products of sums using k maps and don't care F = (A, B, C, D) =…

A: Solution:- Don't care is not given in question.

Q: cout << x; in order to show all elements

A: Given :- In the above question, an array is mention in the above given question   Need to use cout…

Q: Q2) Simplify the following function for F using a K-map. F(A,B,C,D) = E m(0, 2, 8, 10, 12, 14)

A: solution of the given function is-

Q: We are given two automatons for the following problem: Left automaton = {w E {a, b}" : w is empty or…

A: SUMMARY: - hence we discussed all the points.

Q: For the non-recursive towers problem, we used an array of vectors to represent the towers: vector…

A: According to the information given:- We have to find out the correct option that satisfy the given…

Q: A valid argument is given below. Fill in the missing values of the proof. vx (R(x) v Q(x)) 3X (P(x)…

A: According to the information given:- W have to find the valid argument for A,B,C,D

Q: if q=[1 5 6 8 3 2 4 5 9 10 1],x=[ 3 5 7 8 3 1 2 4 11 5 9] then: a) find elements of (q) that are…

A: Required:

Q: give set of R(x): x < x^2 where the domain is Z

A: give set of R(x): x &lt; x^2 where the domain is Z

Q: Write the following as proposition: For every integer n, there exists an integer m such that m > n2

A: Here in this question we have given a english sentence and we have asked to convert it into…