2. Let C be the circle |z −1 < 2 taken in the positive sense. Evaluate the following integrals: sin(z + 3) (z + 3)² Jo a. Jo dz b. cos z cot z dz

Q: (a) An (B − A) = Ø.

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

Q: 2.5.22. Let A, B,C be three sets. Prove that if A \ B C C, then A \C C B.

A: Given: Let A,B,C be the three sets. A-B contained in C

Q: 2 > ]x – 4| X-1

A: Given,          2x-1≥x-4

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: -8. a. Show that if A and B are independent, then P(A|B) = P(A). b. Say we have sets A, B, and C (do…

A:

Q: 13. Find the Cartesian product A x B of the sets A = {12, 9, 10} and B = {14,4}

A:

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: Prove that every well order is a linear order,

A: A set  is said to be well-ordered if it has a total order and has the property that every non-empty…

Q: help.

A:

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

A:

Q: 20 Let A = 11 then A-1-

A: Given: A matrix A=2011. To find: A-1

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

A:

Q: Are u sure its not 1

A: It is given that a=0 and b=1.

Q: 2. Use a table to express the values of each of these Boolean function. F(x, y, z) = x+yz

A:

Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

Q: . How many relations are there on the set S = {2, 4, 6}? 892 512 none of these 1024

A:

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

A:

Q: Show that if S x T is a closed subset of R2, then S and T are closed subsets of R.

A: As per the question we are given two subsets of R i.e. S &amp; T and we know that the set S × T is…

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

A:

Q: Let ā= . Find |āà.

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

Q: Boolean unc B + AB'C + BC

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: O Is the set S=\[1.2], [-4 2. abaris for R?.

A: We know dimension of ℝ2  is 2  this implies basis of ℝ2 contains two linearly independent vectors.…

Q: 2. Let A = and B = al. Show that det(A + B) = det A + det B if and only if a + d = 0.

A:

Q: 3. Show that 1 > 0. 4. Show that if a > b and c < 0, then ac < bc.

A:

Q: Find P(C1)  l. Find P(V4)  m. Find P(C1 ∩∩ V4)

A: As per guidelines we are allowed to solve maximum of 3 sub parts If you need help with other…

Q: Let P(C|D) = 0.2, P(D) = 0.3 and P(C|D) = 0.4, then C and D are Select one: a. disjoint b. not…

A:

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: - If A = {2,3} and B = {x | x ≤ Z+,x <3}, then A x B= Select one: O a. {(1,2), (1,3), (2, 2), (2,3)}…

A: Given that the setsA=2,3 and B=x | x∈Z+ , x&lt;3

Q: Let S = {-2, -1, 0, 2, 1, √2, 2, 4). Determine which elements of S satisfy the inequality. ( 2-1 2x

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Q: . Find the sets A and B if A - B = {1, 5, 7, 8}, B-A = {2, 10), and An B = {3, 6, 9).

A: