VI. De-Morgan's Laws : If A, B and C are any two sets, then (i) (A U B) = A'O B' (ii) (An B) = A'U B'

Q: What are the right three digits of 3402? Hint. Use Euler's theorem. What is o(1000)?

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Q: _If A = Verify that [A-!]" = [A"]¬1 ? l1 2.

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Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: 1. Prove that the followingn is a theorem in SD. Av - A

A: Theorem :-

Q: (2) If BC À. then P(B| A) P(B) P(A)

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Q: If continuous or f differentiable is [ Select] on [a , b] then the [Select ] integral of definite or…

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Q: Let x € Z. Prove that if 3x + 7 is even then x is odd.

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Q: Is Statement (1) below True or False and WHY? TEA=B is equivalent to "TEA IFF TE B"

A: Let us provide justification and check whether both equations are equivalent or not

Q: Let a e Z. Prove that if 6 | a and 10 | a, then 15 | a.

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

A: Given  a, b and m are positive integers.  (a, m) = (b, m) = 1.We have to prove that (ab, m) = 1.

Q: Let x € Z. Prove that if 3x + 7 is even then x is odd.

A: , then we have to show  is even then  is odd

Q: Prove that if A and B En and Ac B, then

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

A: Given: A be m*n matrix

Q: Suppose a, b e (0, ) and a b- a.

A: I hope that this solution will help you .Thankyou. Best regards.

Q: If z1:2., are complex numbers such that =|= =. = |=,| =1, Prove that

A: To prove: z1+z2+…+zn=1z1+1z2+…+1zn Given: z1=z2=…=zn=1 Since, (1) zz¯=|z|2 (2) z=z¯

Q: are in A.P., b, c, d are in G.P. and at a, c, e are in G.P. -10 - e

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Q: verify that (AT )T = A

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Q: Let ā= . Find |āà.

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

Q: Prove the following claim: At least two powers of 3 have exactly 100 digits

A: The number of digits in an number x is log10x+1, where · is the greatest integer function. The Claim…

Q: 3 I- 0) = [u- w -3 [-1 4] 6.

A: We will solve it in parts Consider 0-1453-101-1 = (0)(5)+(-1)(-1)+(4)(1)    (0)(3)+(-1)(0)+(4)(-1)=…

Q: Suppose gcd(a, b) = 1. Prove that ab | c if, and only if a|c and b| c.

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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: Given A = 03-2 00 1 compute et.

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Q: Suppose that P(A;) = 1 for all i = 1, 2, .... Show that P(N A;) = 1.

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Q: Let a e Z. Prove that if 7 | 2a, then 7 | a.

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Q: Evaluate the following E jOO) i() ())]

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Q: Let A =| 0 -3 0 . Compute A“. 5

A: A=2000-30005 Now,…

Q: Prove that du Inlul + C where n= -1 u

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Q: Obtain the values of In(/3 – i).

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