28. Find the Boolean product of A and B, where [1 0 0 17 A =0 1 01 1 1 and B =

Q: 29. Compute det B, where B = 1 2 2

A:

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: The Boolean sum of the variables z, y and z or their complements, that has the value 0 if and only…

A: Given x=0y=1z=1 Thus yc = 0zc = 0 We know that  a+b = 0 if and only if both a and b are zero

Q: o is a) 1-1 b) onto c) Both 1-1 and onto d) None

A:

Q: Compute A?x and A3x the correct way: ´1 0 () 0 1 A = 3 0 2 0 1 1 1

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Q: The equivalence of the Boolean expression: z= x(x+ y) is A z= x(xy) B z=xy C := xy D :=x(xy)

A: Given Boolean expression                                                        z=xx¯+y¯ we have to…

Q: 3. prove that: det (AB) = det (A) det (B) If a - (;). » - ( :) 2 -1 7 A = 3 2 4

A:

Q: 3. Show that if A-1 exists, then f eAT dr = A-(eAt – I) = (e4t – I)A-1.

A:

Q: 3 Let A = -6 -1 -2 and v = -6- -2 3 Av = -6 2 -9 Ex: 5 s v in null(A)? Select an option

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Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: 2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and…

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Q: 4 1 0 Let X be N , ( μ. Σ ) with 1 30 0 0 2 Examine the independence of the following : (i) X, and…

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Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: (d) The apartment is hot if and only if the temperature is not 75º and the air conditioning is not…

A: Here given Statement in English convert them to symbolic form using standard notation

Q: If X(z) = In(z - 2), then what's x(k) а. O b. ak O C. -ak / k d. others е. ak / k

A: Z transform and inverse Z transform

Q: 3. Is this sentence consistent? “There is someone who loves exactly those people who do not love…

A:

Q: 6. Use a table to express the values of each of these Boolean functions. а) F(x, у, 2) —7 b) F(x, у,…

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Q: ne set {u1, u2, U3} is orthonormal. 1 2 V5 2 ,u2= 10 1 ,U3= 1= 10

A: The condition for the vectors to be orthonormal is that the  magnitude of each vector is 1 and the…

Q: 4. Let b > a > 0. Show that (a,b] is neither closed nor open.

A: Explanation of the solution is given below....

Q: 2.1. Prove that B Is erse of A -17 11] -7,B: 0 3 2 [1 1 2 2 4 -3 [3 6 -5] 2 A = -1 11

A: To prove that B is the inverse of A.

Q: O prove that Using Boolean algebra Ā+ABč + AB+BC 1

A: In this question we have to prove the following using boolean algebra. NOTE: As per our policy we…

Q: iken that I+2=1 xpressyin terms of xand z.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

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: 2 Let A = then det(3AT) - 18 -6 -2 II

A:

Q: Show that 2"=nCk and 0 = [(-1)^nck k=0 HINT: Consider(1-1)" and (1+1)" k=0

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Q: 3. Show that if A-1 exists, then eAT dr = A-1(eAt – I) = (eAt – I)A-1.

A:

Q: 7. Use Boolean Algebra to prove that- A.(B + C ) + A (C + B ) = A

A:

Q: The following are equivalent in a Boolean algebra: (1)a + b = b.(2)a * b = a.(3)a' + b = 1,(4)a × b'…

A: (3) The given equation is: a'+b=1

Q: 21. Compute A100, and A-1, where A 5 0 0 -3 -2 0 -305

A: given matrix A=50-30-20-305 compute A100 and A-1

Q: 1- Simplify the following Boolean expression using algebra. a. X'Y' +X'Y + XY = B. A'B + B'C" + AB +…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A and B cannot c are independent

A: For independent events : P(A n B) = P(A) * P(B)  And P(A u B) = P(A) + P(B) - P(A n B)  For mutually…

Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

Q: discrete

A: In method of contradiction we start by assuming that given statement is false. Then prove that it is…

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

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Q: The dual of the following Boolean expression is (0 +1)(1+ yz) + 7 O (1.7) + (0.y + 2). z O (1.7) +…

A: We have to find the dual of 0+x1+yz+x

Q: 2. Verify that det(AB)= det(A)det(B) and determine whether the equality det(A+B) = det(A) + det (B)…

A: Note : As per the authoring guidelines, when multiple questions are posted, then only first question…

Q: 3. prove that: det (AB) = det (A) det (B) If 2 -1 7 2 B = A 3 2 -3 4

A: In the question it is asked to prove the property det(AB)=det(A).det(B). Where A=2-132 and B=72-34

Q: 4. Let 1-a a P = 0 < a, b < 1. 1-6 Prove (:) (1 – a – b)" 1 b a a -a a +bb a a +b -b b

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Q: 4.2. Let a, b E Z, where a 0 and b 0. Prove that if alb and bla, then a = b or a = -b. -b.

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Q: ao + 2a1 + a2 - azz²) = | da0 + 7a; + 5az 3ao + 5a, + 5a2, Let T(ao + a;7 - Determine ifT is…

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Q: Show that r(r+3) Hence, Show that 1 +. 2.5 1 1-4 3-6 n(n+3) n+3 n+2 n+1

A: Using series

Q: 4.2. Let a, b € Z, where a + 0 and b + 0. Prove that if alb and bla, then a = b or a = -b.

A:

Q: Q1) Compute the products using the definition as a linear combination. 8 3 -4 1 2 1 5 1

A: As per the definition of linear combination abcdef.x1x2x3=x1.ad+x2.be+x3.cf

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: 0. Prove that (i) |4' ||, =||4||,, and (ii) ||4' A|| -||4|-

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Q: Prove that if c=12n+4 where n in Z then c is not a linear combination of 27 and 18

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Q: ieN 6. (a) Uto, i+ 1] = (b) N[0,i+1]= ieN ieN 7. (a) URx[i,i+1] = (b) ORXlii+1l=

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Q: 2. Find U, A, and NE,Ą, where: a. A = {-i, i} for every positive integer i. b. A = {i°, i', i²} for…

A: