1. Let C be the circle |z − 1| < 2 taken in the positive sense. Evaluate the following integrals: Jo a. e² - e (z − 1)² dz b. -1 (z-1)100 (z - 4) Jotz-1 dz

Q: 2 Let A= then det(3A") = 6- -2 - 18 -6

A:

Q: (a) An (B − A) = Ø.

A: Given data:- The given equation,  A∩(B-A)=φ

Q: Let Find M₁3 and C13. M13- C13- A = 2-4 2 0 Tom- 13 3 -6 3 -7 9 1 -9 7 0

A:

Q: How many individual simple functions make up the following composite input? 2 1 5 6 A) 4 в) 5 c) 6…

A:

Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

A:

Q: Let S be the set S={(x+y) l 2x+3y>=(greater than or equal to) 12} What would be Sc  (S complement)…

A: The given set is: S=x,y∈ℝ2 | 2x+3y ≥12 Cleary S⊂ℝ2.

Q: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: et z = 6ex²y³ find O 12xy³ex²y³ O 18x²y²ex²y³ O 18xy³x²y³ O 12x²y²ex²²³ дz ax

A: Given, z=6ex2y3

Q: C. Show that both R and R² may be covered by countably many open balls.

A: Firstly we have shown that R may be covered by countably many open balls. Let us  consider the set…

Q: Using a decoder and external gates, design the combinational circuit defined by the following two…

A:

Q: Let A, = {..., – 2,- 1,0,1,...,i}. Find

A: Ai={..., -2, -1, 0, 1, ......, i} ∩i=1nAi=?

Q: 4. Let A = of O 2| Calculate

A:

Q: AC Biff P(A) C P(B).

A:

Q: fond the dertive YfY-V5R-47

A:

Q: Prove ImA = A = Aln if A is m X n

A: Given: A be m*n matrix

Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

A:

Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: 10 8 8. 6. 4. 4. 12 12 4. 4. C 8. 3 10 10 Which is similar to X? 5. 3.

A:

Q: E. Show that both R and R² may be covered by countably many open balls.

A:

Q: Let S = (a, b, c, d, e, f with P(b) = 0.16, P(c) = 0.12, P(d) = 0.29, P(e) = 0.22, and P(f) = 0.11.…

A: Given S = { a, b, c, d , e , f } P( b ) = 0.16P( c ) = 0.12 P( d ) = 0.29 P( e ) = 0.22 P( f ) =…

Q: X and  Y are randam variables then XeY is a randam variables.

A: Here, The X and Y are two random variables  Then XeY are also random variables we have to show Here…

Q: Let U= {x |x E N and x< 10}. Let A = {x | x EN and x is odd and x< 10}. Let B = {x |x EN and x is…

A:

Q: Let A = { {a}, {b}, {c}, {d}, {e} } Determine by extension P(A

A:

Q: find z trans foyms of folleing -an simwn ĭ

A:

Q: Let ā= . Find |āà.

A: Here we will find the magnitude of vector a,

Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

A:

Q: 2. Let f and g be any permutations. Show that the order of h = fgf- is the same as the order of g.

A: Here f and g are tow permutations  and we are given that h=fgf-1. We have to show that both f and g…

Q: If then A-¹- = A = [1 0 0 07 3 1 0 0 24 1 0 8 55 1

A: The given matrix, A=1000310024108551 We have to find an inverse matrix of A.

Q: a PDE from the following- @u =f() Form メソ

A: We eliminate the arbitrary function f from the given equation to form the required partial…

Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a&lt;b means that a…

Q: Suppose that P(A) = 0.4, P(B) = 0.3 and PAUB)-042, then a. A and B are dependent b. none of the…

A: We have to find out correct answer...

Q: 4. Let A

A: Given,                A=1, 2, a, b, ϕ

Q: Show that both R and R² may be covered by countably many open balls.

A:

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: The Human Resources office in a company observes the pattern of absences of employees by days of the…

A: Given: The company has 100 employees and over 10 weeks (5000 employee appearances) they notice that…

Q: Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.25, P(d) = 0.2, P(e) = 0.1, and P(f) = 0.11.…

A:

Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: Let S = {a, b, c, d, e, f} with P(b) = 0.13, P(c) = 0.19, P(d) = 0.3, P(e) = 0.12, and P(f) = 0.15.…

A: P(a) = 1 - {P(b)+P(c)+P(d)+P(e)+P(f)} = 1 - (0.13+0.19+0.3+0.12+0.15) = 1 - 0.89 = 0.11 So, P(a) =…

Q: Let id (2,-2, 1), d= (2,-1,-6). Find i ,-dand |M.

A:

Q: Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than…

A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove &lt;-…