Translate the following statements into idiomatic English where the domain consists of all (romantic) couples of persons, M ( x ) = x is married, and C ( x ) = x has children. Which statements are (in fact) true/false?   ∀x ( M ( x ) → C ( x ) ) ∀x ( C ( x ) → M ( x ) ) ∀x ( M ( x ) ∧ C ( x ) )

Q: Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y):…

A: Given W(x): ' x is a woman' M(y):' y is a man'

Q: For the predicate P(x, y) ::= [x + 2 = y], choose all the pairs of x and y such that P(x, y) is…

A: Given query is to find the correct option for the expression.

Q: (avb)л (aVc) d → e (bA c) → (F → k) ^ c) .. -F

A:

Q: 1) Let A = {Ø,0, {1}, {0,{1}}}. Answer by true or false to the following statements: ii iii iv V…

A: Power set: A set PA is said to be a power set of a set A if it contains all the subsets of the set…

Q: Determine det(A) Determine adj(A) -3 -2 -3 +00 A = 1 4 6 0 -1 3

A: given matrix is A=-3-2-314360-1

Q: Find JA|, |B|, AB, and |AB|. 1 4 2 -3 0 A = -2 -4 1 B = 1 -1 3 3 1 2 11 (a) JA| (b) |B| (с) АВ (d)…

A: Find the determinant

Q: Show that Hh - Va! 1 -1 can be written as hlVx+h x/x+h+V¤(x+h)

A:

Q: Given Q(x, y) means "x and y are real numbers such that x + 2y = 5", evaluate Vx3y Q(x, y) O True O…

A: Given that, Q(x, y) means "x and y are real numbers such that x+2y=5",

Q: If m ∠ D R C = ( 5 x + 42 ) ∘ and m ∠ C R A = ( 2 x + 75 ) ∘, then x =____?

A: Given,         ∠DRC=5x+42° and ∠CRA=2x+75°

Q: If B C A, then (i) P(AB)=P(A) - P(B), (ii) P(B) ≤ P(A)

A:

Q: Which of these statements is the inverse to Vx e People, HavePhD(x) A Teachln(x, university) →…

A:

Q: If o = (r x a) (r x b), show that Vo =bx (r x a) +a x (r x b)

A:

Q: show that |z3|  ≠ |z4|  it is verified that |z1+z2/z3+z4|  ≤ |z1|+|z2|/|z3|-|z4|

A:

Q: Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

A: The symbolic is given as follows: ∃x∀y¬Nx∧Wx∧Ry→¬Fx,y We are given that: Fx,y: "x is friends with…

Q: [6 -3 Evaluate | A | for A = 2 3

A: |A| represents the determinant of the matrix A. Let a matrix X=abcd, then its determinant is given…

Q: 1. Translate these statements into English, where the do- main for each variable consists of all…

A: a) for all x, there exists y such that x is less than y b) for all x, for all y if (x is greater…

Q: Show that the following two sentences are not equivalent in FOL : ¬∀x(A(x) → ¬B(x)), ∀x(A(x) →…

A: Introduction: In logical reasoning, two statements are referred to as logically equivalent if their…

Q: (p v q) → r = O (p v r)^(¬q v r) O (-p v r)v(q v r) O (-p v r)v(¬q v r) O (-p v r)^(¬q v r)

A: We will find out the required value.

Q: Use quantifiers, logic symbols, and English to translate the following: (a) Every positive real…

A: We need to translate the following sentences.(a) Every positive real number has a positive real…

Q: Let the domain of x and y be all people. Let W(x): "x is a woman", M(y): "y is a man", and Lex.y):…

A: The objective is explain the meaning of the statement ∀x∀y Wx∧My→Lx,y

Q: 3. Choose whether the following statements are true or false: (a) Ax.ly.y x is a-equivalent to…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Give a statement of the form V XED, P(x) Q (x) Such that its original, converse, inverse and…

A: We need to prove the original and converse statement of ∀x∈D,P(x)→Q(x). First, we need to understand…

Q: -3x+7 for x < -1 Let g(x)=x² +3 for-1<x<4 5 for x ≥ 4 Evaluate: i. g(3) ii. g(-2) iii. g(-1) iv.…

A: Topic = Function

Q: ||x+y||?+||x-y||?= ||x|2+||y|² O 2(1시7+ \»1) o 2(||² - ||") .

A:

Q: State the scope of each quantifier in the following expression: "Vy, [Q(x, y) ^ 3r (R(x, y) ^ ~P(x,…

A: The quantifiers used in the expression are ∀,Q, R, ∃, ~P. The scope of the quantifiers are given…

Q: Write a logical proof to prove that the following argument is valid. Væ(P(x) → Q(x)) Jæ (R(x) ^…

A:

Q: Which of the following statements is correct? a) P(X | Y) = P (X) if X and Y are independent.

A: Our aim is to find the correct statement.

Q: The first-order logic formula vx A(x)^3y -A(y) is satisfiable but not valid

A: Given that a first order logic formula ∀x A(x)∧ ∃ y¬A(y). We need to check that is it valid,…

Q: If X= { a, b, c, d } and Y = { f, b, d, g},      find. (i) X – Y           (ii) Y – X          (iii)…

A: The given sets are

Q: Give an example of an open sentence (x, y) so that the quantified statem xy, P(x, y)) is True, while…

A:

Q: Vx P(x) is equivalent to Vx ¬P(x). O True O False

A: ¬∀xP(x)≡∃x¬P(x) but it is given that  ¬∀xP(x)≡∀x¬P(x)

Q: Use rules of inference to show that if Vx(P(x) (Q(x) A S(x))) and x(P(x) ^ R(x)) are true, then…

A: In the given question we have to prove that the statement R(x)∧S(x) is true when (P(x)∧R(x)) is true…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.