14. A set SCR is closed if and only if S'CS.

Q: If the order of a group G is p²q² with p and q as distinct primes, then G is not simple.

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Q: Prove that if a o-algebra of subsets of R contains intervals of the form (a, o), then it contains…

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Q: Ex. 1b Given: C is the midpoint of AE and BD. BD CD AE Prove: AC Statements 1. AEBD 2. AC=CE,&C=CP…

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Q: Prove that

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Q: 4. Give an example of an indefinite quadratic form on R³ whose corresponding symmetric matrix has no…

A: Let Q(x1,x2,x3)=-x12-2x1x2+6x1x2+3x22-2x2x3-x32 be a quadratic form whose symmetric matrix is…

Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: eimil 2.5 THEOREM Suppose f : D R and g : D→ R, xo is an accumulation point of D, and f and g have…

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Q: If F(s) = 1/(S-2), then f(t) is %3D a) e²'u(t) c) u(t-2) d) e"'u(t) -2t b) u(t +2)

A: Given Fs=1s−2 We have to find the ft Use definition of inverse Laplace transform, which is given…

Q: Theorem: let S₁, S₂ be the collection of sets D (US) U (US). = US. SES, VS₂

A: Solution: Let S1  and S2  be  the  collection of sets.We  have  to show  that  ∪S∈S1S∪∪ sS∈S2=∪…

Q: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

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Q: 29. For any odd integer n, n° n² +3 %3D 4 4

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Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

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Q: For any two events A and B; P (AUB) = P (A) + P (B) – P ( A nB) %3D

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Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

Q: 10. The supremum of a non-empty set S, if it exists, is always unique.

A: We need to prove that Supremum of a non empty set S, if it exists, is always unique.

Q: Prove that

A: Here given  limn→∞xnn! for any real number x.

Q: Every cyclic group is necessarily abelian but the converse is not necessarily true

A: .

Q: tan? Asin? A= tan? A-sin?A %3D

A:

Q: By setting up a formula for Riemann sums, and then taking their limit, 1 | (20-2) (2a – a²) dæ .…

A: The given definite integral is…

Q: Establish that if a is an odd integer, then 2" a“ = 1 (mod 2" *2) for any n 2 1.

A:

Q: Please prove it

A: Given information: The investigator is specially interested to estimate the parameter u of a…

Q: Let f [a, b] → R be a bounded function. Then the followings are equivalent. (a) f [a, b] → R is…

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Q: (1-sinA) (1+sinA) =(secA-tanA)

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Q: Example 1a Given: L1 L2,L2 &L4 form fin. pair/1 &L3 form lin. pair. Prove: L3 L4 Statements 1.41€…

A: The given data is: ∠1≅∠2  To prove: ∠3≅∠4

Q: a? b? +c? b? c? +a² cʻ +a' = 0 S c2 a? +b?

A:

Q: Let (X, M, μ) be a measure space and (Y, 7) be a topological space. Let f: X→Y be a function. Set Ω…

A: Definition : Let X be any set  and F be a collection of subsets of X . We say that F is a σ- algebra…

Q: -) Let dim(V) = n. Let T : V → V be a linear operator. Let W1, W2 C V e T-invariant subspaces.…

A: given dimV=n , W1,W2⊂ V be a T-invariant subspace. suppose V=W1⊕W2 let β1=w1,w2,....wk be an ordered…

Q: 3i16 - 103 1+i 2i84 + i79

A: given the expression 3i16-i1032i84+i79 we know that i2=-1…