Identify the error or errors in this argument that supposedlyshows that if ∃xP(x)∧∃xQ(x)is true then∃x(P(x)∧Q(x))is true. ∃xP(x)∨∃xQ(x) Premise ∃xP(x) Simplification from (1) P(c) Existential instantiation from (2) ∃xQ(x) Simplification from (1) Q(c) Existential instantiation from (4) P(c)∧Q(c) Conjunction from (3) and (5) ∃x(P(x)∧Q(x)) Existential generalization

Q: 8.0 Prove the Invalidity of the following argument: 2022/12/9 (x) [Qx(Rx Sx)] (3x) (Tx-Rx) (3x)…

A: As per the question we have to prove the invalidity of the following argument : (x) [Qx ⊃ (Rx • Sx)…

Q: x+ 6x +7 f(x) = {-x + 3 5 if x < -1 if -1<x<3 if x 2 3 f(2) = %3D f(-1) = S(-7) = S(3) =

A: The given step function is f(x)=x2+6x+7if x&lt;-1-x+3if -1≤x&lt;35if x≥3

Q: Let n(B) = 5 and n(AUB) = 7. (a) What are the possible values of n(A)? (b) If n(An B) = 0, what are…

A: Let A and B be two sets , then  n(A∪B)=n(A)+n(B)-n(A∩B) . Given that n(B)=5 and n(A∪B)=7 .

Q: The expression of the statemer All dogs (D) have fleas (F) using quantifi ers is

A: D(x) be x is a dog F(x) be x has fleas

Q: Which of the following is equivalent to - (Vx (P(x)VQ (x?),

A: we will use demorgan law here 1)   ∼(P∧Q)=(∼P)∨(∼Q) 2)  ∼(P∨Q)=(∼P)∧(∼Q)

Q: Q.No.5. Let P(x) be the statement "x can speak English", Q(x) be the statement "x knows the computer…

A: The logical connectives are:

Q: Here, p(t)=0,q(t)=| and in , and g(t)= the interval that contains t= -1 is so q (t) is discontinuous…

A: To find:Determine the longest interval in which the IVP ty" + 3y = t, y(-1) = 1, y'(-1) = 2 has a…

Q: 67. (x + 1)(x + 1)(x - 1)(x - 1)

A: Rearrange (x+1)(x+1)(x-1)(x-1) as (x+1)(x-1)(x+1)(x-1) and then use the algebraic formula,…

Q: (4) For each of the following claims, give its negation in math symbols. (Do not use A.) (4.1) (V…

A: Given logical statements are  1) ∀x1,x2∈A∃x3∈BPx1,x2⇒Qx32)∃x1∈C∀x2∈D∃x3∈ERx1,x2∧Sx2,x3.

Q: What is the domain of the relation x(x-3) ? {(X,y): y = (x+4)(x-7)). ) {x: x = R, x -4, x > 7} ) {x:…

A: Domain of function f(x) is the set of value of x for which f(x) is defined.

Q: Quantifications are negated as P(x)=xP(x) P(x)=x¬P(x) (a) Let P(x) be" x+1>x ." What are the…

A:

Q: Is the following a syntactically correct X-calculus expression? ((lambda x.(lambda y.(x + y))) 5) 6)…

A: We have to check either the lamdax.lamday.x+y56 correct λ-calculus expression.

Q: Find the domain of f(x)= Mostly sunny x|x€Rx‡¬ √10} 00 x|x€R_x#√10} Ox|x€R¸x*-√√10, 10}…

A: a2 - b2 = (a - b)(a + b)  and 10 = (10)1/2(10)1/2

Q: 10. Let C(r) be the statement " has a cat," let D(z) be the statement " has a dog," and let F(x) be…

A: Note: As per the honor code, only one question can be solved at a time and up to 3 sub-parts only.…

Q: Q3.1 Write the following statements in English sentences. (1) The negation of If p is a prime…

A: We are authorised to solve only one question, please repost remaining questions. Mathematical…

Q: 3 4 gla) - 4 17 3 A) s '(x) 3 A) Yes B) No -2.x + 8 B) f (x) – 3 C) s '(x) – x – 1 2 3) Sl:) – VI+2…

A:

Q: negation rules of (a) Give an example of a pair of predicates P(x) and Q(x) in some domain to show…

A:

Q: Let U₁ = (b) (c) 5 (d) , սշ 2 3 Compute each of the following. (A graphing calculator is…

A:

Q: D(x): x can drive F(X): x is in my family The universe of discourse consists of everybody in my…

A:

Q: if f(x) = 0 < x1 < 1, 1< x2 < 2, then fi (x1) = x2, f2(x2) = 1 True False O

A:

Q: If 4x − 2x² <f(x) <x² - 2x +3 for - all real numbers except for x=1, then

A: We have to solve given Questions.

Q: What is the result of this Lambda expression? (λ(x) 4 * 2x + 3x)  (2)

A: The lambda expression (λ(x) 4 * 2x + 3x) defines a function that takes a single argument ` x ` and…

Q: Evaluate (x + 5)(x − 1)(x − 2) (x - 1)(³) — 2(x − 1)(²) O A (x − 1)(³) + 2(x − 1)(²) (x − 1)(²) —…

A:

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: Determine whether (5) () = (;) (") n-3 (where 3 < k < n) is true or %3D false. O True O False

A: We have given that

Q: Suppose that the domain is the set of all integers, which of the following are propositions? There…

A: Proposition in mathematical logic is, a statement that evaluates true or false.  If P and Q are…

Q: 3. Suppose that the domain is the set of real numbers. Consider the following predicates. Z(x): "x…

A: Given that domain is the set of real numbers. Z(x): “ x is an integer” R(x): “x is a rational number…

Q: Which of the following statements below are true for f(x) = - 2(x - 1)(x - 2)(x + 3)(x + 4)? * i) as…

A:

Q: the statement (3x)A(x) → A(z) where z is a new variable not free (not an “input variable”) in A(x).…

A:

Q: f(z) = 2(x – 5)² + 3. - f (x) is invertible for which values of x?

A: Given function is: fx=2x-52+3 Then we get,…

Q: 1. Let P (x) be the statement "x = x²." If the domain consists of the integers, give True/False…

A: We have given a statement ,  P(x) : x = x2 Here , domain consists of the integers , that is x ∈ ℤ.…

Q: (a) Let r(x), s(x) be given by r(x): x is odd s(x): x² - 1 is even The statement "If x is odd, then…

A:

Q: Suppose f(x). Evaluate: 1 5- -x A -21n|x - 10| + c B ® -n|x- 10| + C +C +C

A:

Q: (b) Determine whether the following statements below is true or false. universal set = {0,1,2}…

A:

Q: H(x) denotes " is a horse." U (x) denotes "x is a unicorn." B(x) denotes "x is blue." C(x,y) denotes…

A: handwriting solution

Q: Let gcd(a, b) = d then which of the following is correct (i) dla (ii) d|b (iii) d[(ax + by) (a) only…

A:

Q: If f (x) = 1 x-7 then f-1 (x) =2x+7                   2                    2) If f (x) = {(-3,1)…

A:

Q: 7) Master Theorem Usage, II Homework f (1) = 1 and f (n) = f(;) + 2v ñ

A:

Q: consider the statement (formula) (3x)A(x) → A(z) where z is a new variable not free (not an "input…

A:

Statements and Logic

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