2. Find the values, if any, of the Boolean variable x that satisfy these equations. a) x ·1 = 0 c) x ·1 = x b) x +x = 0 d) x ·x= 1

Q: Prove that: 1- Ā. (B × C) = B . (Č × Ā) = C . (Ā × B)

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: 18. Prove that A × (BUC) = (A × B) U (A × C).

A: The objective is to solve the above question.

Q: (c) Prove or give a counterexample: Assume E as well as IT is satisfiable. Is Enr satisfiable? (d)…

A: given Boolean formula , we have to to prove is given condition in question is satisfiable or not .

Q: A AB

A: Is AB is congruent AD what theorem is used to prove this?

Q: Show that if AB = AC and A is nonsingular, thenB = C.

A: Given that  A is invertible matrix. It means inverse of A matrix is possible. A is non-singular…

Q: Assume that u - v = 2, ||u|| = 8, and ||v|| = 3. Calculate the value of (9u + v) · (u – 8v). %3D…

A: we multiply the given equation and then put the value of given data. u=8 v=3 u.v =2 note- According…

Q: Show that following formulas can be deducted in Hilbert System (It is allowed to use Deduction…

A: We have to prove the given formulas by Hilbert system

Q: Assume that u · v = 5, ||u|| = 9, and ||v|| = 4. %3D Calculate the value of (3u + v) · (u – 10v).…

A:

Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

A:

Q: Use proof by contradiction to prove that if x + y > 2, then x > 1or y > 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: Prove that (a; + b;) = a; + i= 1 Σύ. i=1 i=1

A:

Q: prove the ged (atb,a?+b³) =16Y2 assuming that gcd (a,b) =1 •

A: It is given that gcd(a,b)=1

Q: Verify the &-ô identity: Ejkɛipq = djpôkq – djqðkp. Then use this identity to show that (a) EilmƐjlm…

A: The given identity is εijk εipq=δjp δkq-δjq δkp  where the εijk is called the alternating tensor or…

Q: 1- Suppose A=

A:

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

A:

Q: BC = a. Prove: AB = 2a and AC = aV3. %3D %3D

A:

Q: (b) The support of (U,V), namely the values of u and v that correspond to the non-zero part of…

A:

Q: 1. Use a two-column proof to prove the equivalence below -(P V-Q) v (-PA-Q) = ¬P

A: We will use basic equivalence laws of logic

Q: 3. prove that: det (AB) = det (A) det (B) a - (; ), » - ( ) 2 -1 7 2 B = 2 в 3 %3D

A:

Q: Prove that |A U B| + |A n B| = |A| + |B|

A: Let A and B are two sets. A = number of elements in the set A. B = number of elements in the set B.…

Q: (a) Prove that de 2n a>b>0 Jo a+ bcose Ja? - b2

A: We will use basic knowledge of Integral Calculus and trigonometric identities to solve this…

Q: prove that n E vol(B6)) > II(b: – a;) vol( B jEJ i=1

A:

Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: Use a proof by contraposition to show that if x + y ≥2, where x and y are real numbers, then x ≥1 or…

A:

Q: If a is transcedental over Q then a^2 is also transcedental over Q

A:

Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

A:

Q: Prove (A N (B U C) = Ā U (B U C) %3D

A:

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: (a) Prove the following property: (:) - (.".)

A: Hey, since there are more than two questions posted, we will answer the first question. If you want…

Q: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…

Q: 9. Prove that the following pair of formulas are equivalent in SDE. U → -(E V D), (-E A ¬D) →¬U

A:

Q: 6. Prove that |x.y| = |x|.|y|, where x and y are real numbers.

A:

Q: Q1/ Prove that (Sa,0) is not Comm Sroup.

A: To prove the non commutativeness of the group

Q: Prove that AxCBx)=A.2)B CA. B)T wheve. Aca,itazj+ask Babiitbijab3k

A:

Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: Prove by logical equivalences and rules of inference that vx(L(x)→ R(x)), 3x(P(x)^ ~ R(x))E ~(P(x)→…

A: Rules of inference are the tools to prove logical equivalence. This method of proof excludes…

Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

Q: (a) Prove that if f e C (R²) then a (af af %3D

A: This is a problem of the calculus of several variables, higher dimensional calculus.

Q: If X ∼ N (μX , σ2X) and Y ∼ N (μY , σ2Y ) are independent, then prove

A: X~Nμx,σ2x and Y~Nμy,σ2y are independant

Q: Given   KB = (X→Y) ∧  (Y→Z), and   α  = (X→Z) Is KB |= α is valid or not?

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 15. Complete the proof of Theorem 1. (ASsume B-A-C, then obtain a contradiction.)

A: Theorem-1: If A−B−C then C−B−A, and neither A−C−B nor B−A−C.A−B−C means that A,B and C are distinct,…

Q: Suppose AnB CC\D and x E A. Prove that if x eD then x ¢ B. (Hint: prove via contrapositive)

A:

Q: Under what conditions on A and B is (AB)-1 = A-1B-1? Prove your assertion

A: Assertion: If A and B are commutative, then  AB-1= A-1B-1.

Q: Prove that if C is equivalent to B and B is equivalent to A, then C is equivalent to A.

A: The relation 'R' = 'is equivalent to' is transitive. Therefore if x R y and y R z then x R z.

Q: Prove that Q (1 + i) belongs to Q (4-i)

A: Prove that Q (1 + i) belongs to Q (4-i)

Q: O Compute z = (1-i)"(13+i)

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.