The expression P(A u B) = P(A) + P(B) is valid if none of these. O A and B are dependent. A and B are independent. O A and B are mutually exclusive.

Q: (c) Give the contrapositive, the converse and the inverse of each of the following statement: i. Vx…

A: As per bartleby guidelines we only give first question answers.

Q: Determine whether the statement, 'If r > 1, nPr is less than nCr', is true or false. If the…

A: The formula of permutation and combination. Crn=n!r!n-r!Prn=n!n-r!

Q: EXvyP(x, y) is true when there is an x for which P(x, y) is true for every y. A True B False

A:

Q: Which of the following statements are correct? (Select all that apply.) (xa)* = 2*a³ (xª) = x² ab O…

A:

Q: Let h is the difference between two successive arguments then E2 is identify as

A:

Q: Give a natural deduction proof of 3 x A(x) V 3x B(x) →3x (A(x) V B(x)).

A: To prove: ∃xAx∨∃xBx→∃xAx∨Bx

Q: assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =…

A: Given: P(A) =0.25 P(B)=0.35 P(A∩B) =0.1

Q: The negation of the statement Vx:x²+9 100 O b. (3x:x2 +9 100

A:

Q: 10. Write a valid conclusion for each argument B) TAS C) ys A) r s

A: A) r→srsBy direct reasoning

Q: If f(6)=0 and f"(6)=1, then which of the following statements must be true?

A: Given:

Q: Consider the claim: (Vx € N)(3 y E R)P(x,y) = (3 y E R)(Vx E N)P(x,y). ) What is the domain of the…

A: The given claim is  ∀x∈ℕ∃y∈ℝPx,y≡∃y∈ℝ∀x∈ℕPx,y 1) The domain of the predicate Px,y is ℕ, the set of…

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

A: 3) Choose whether the following statements are true or false: (a) λx·λy·yx is α-equivalent to…

Q: Determine whether the following is true: (a) (b) n+1 Σ₁2²= n · 2n+² + 2, i=1 n i-0 3¹ 1- 3n+1 13…

A:

Q: determine derivitive c(x)=ecos(x^2+1)

A:

Q: Which of the following is equivalent to (p → q) A (q → r) → (p → r} None O True (q→r) A (pq) False

A:

Q: Let x €U = Q and p(x) : 3x² + 5x – 2 = 0. a. Write the following statement: (Vx) p(x) b. Is it true…

A:

Q: The value of the Boolean expression (x + y. z). z © z for a = 0, y = 1, z = 0 is O 1

A: Solution:

Q: By natural deduction, show the validity of Vx (P(x) V Q(x)), 3x ¬Q(x), Vx (R(x) → ¬P(x)) E 3a ¬R(x)

A:

Q: Minimize the following Boolean expression: - e) POR + POR+ P Q R+PQR+P Q R+PQR

A: The given expression is PQR+PQR+PQR+PQR+PQR+PQR Use the formula A+A=1…

Q: Prove if R(a) = (21 – A)*' +hen R(1)– R(µ) = (1H)R(2)R(µ)

A: Given that Rλ=λI-A-1 Let λI-A=Aλ                      . . . (1) So, Rλ=Aλ-1 ⇒I=RλAλ=AλRλ         . .…

Q: Which of the following statements are correct? (Select all that apply.) aªy = (xy)2a O a" = a" - b*…

A: Xa/b=(x1/b) a

Q: Let f(x) = ax²+bx+c, where statements are true? (A) las 8 (B) |bs 8 (C

A:

Q: What values of the Boolean variables x and y satisfy xy = x+ y?

A: We have to use Truth Table.

Q: 3. Determine whether each of these statements is true or false. a) 0 e Ø b) Ø E {0} c) {0} c Ø d)

A: Since this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: am+nu 3. axməyn' if u = (x² + y²)e*+y

A: Problem is related to (m+n)th order partial derivative. Here simultaneous differential needs to…

Q: Analyze and answer the following statements. 1. State whether each bi-conditional is true or false.…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Write the following in the form of: r(x) if s(x)+0 P(x) = q(x)+- S(x) s(x) x'+3x +5 (a) x' +2x' +x -…

A:

Q: Show that the following argument is invalid: 3XF(x) V VyH(y),Vw(H(w) - S(w)) E3y-H(y)

A: The first expression is ∃xFx∨∀yHy. That is this expression states that there exists x such that F(x)…

Q: Determine if the following statement is true or false. Motivate your answer. If Re(z) > Re(w) and…

A: We have to check whether the statements, "If Rez>Rew and Imz>Imw then z>w" Is true or…

Q: Which of the following statements are true? Select all that apply. O V5 = xVx for any value of x. O…

A: We have to find value of x for given function.

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: Prove by resolution that "John likes peanuts" if you have these sentences in the knowledge base: -…

A: Answer is mentioned below

Q: 2. a+b+c=c+b+a is true because of

A:

Q: Show that ∗ : R × R → R given by           a ∗ b → a + 2b is not associative.

A: Given:Show that ∗: R × R → R given by           a ∗ b → a + 2b is not associative.

Q: Which of the following statements are correct? (Select all that apply.) (2*) = 2?ab (z*)* (z*)" a -b…

A: Given: To answer the following correct statementsLaw of Exponents: Formulae(1) amn=amn  ; a>0,…

Q: Let T be the statement Vx E R, 0 < x<1=x-1s 0. 4.1. Write the converse of T. 4.2. Write the…

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: Identify the axiom or postulate that applies to the following statement.     If  x = AB + CD + EF +…

A: We have used the axioms here......

Q: Are E and D independent? Yes O Yes O No Are C and D independent? O Yes O No Find P(D U E) Find P(C U…

A:

Q: Translate the following argument into symbols and prove its validity using rules of inference. No…

A: As per the hint:       C(x) : x is a contractor.D(x) : x is dependable.E(x) : x is an engineer. Now,…

Q: If A is 3 x 3 and det (A) = 0, then select all of the following statements which are true:

A:

Q: Which of the following are always true, and which are not alwaystrue? Give reasons for your answers.…

A: To state whether the statement u×v·v=0 is true or false. Solution: Let u=a1i+b1j+c1k and…

Q: Determine what the independent and dependent variables are in each of the following statements.…

A: We have to find what are the dependent variable and independent variable in the following equations…

Q: (7) State whether each of the fOllowing is true or false and justify your answer: (a) {r e Q :0<r<…

A: State whether each of the following is true or false and justify your answer Given, r∈Q : 0≤r≤2 =0,…

Q: Given P(A) = 0.28, P(B) = 0.20 and P(B|A)=0.28 are A and B independent dependent?

A: Given Data: The probability of event A is: P(A)=0.28 The probability of event B is: P(B)=0.20 The…

Q: 6. Find the duals of the Boolean expression: x @ y, whereх Өу— (х+у)(ху) or х@у%3D(ху) + (ху). а)…

A: Solution

Q: p is true, q is true, and r is false, determine whether each of the following compound statements…

A:

Q: If P(A) = 1 P(B) = 2 and P(A U B) 11 find (i) P(A/B), (ii) P(exactly one of A and B occurs), 12 4…

A:

Q: Let x € U = Q and p(x) : 3x² + 5x – 2 = 0. a. Write the following statement: (3r) p(x). b. Is it…

A: Given that: p(x):3x2+5x-2=0

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.