A is closed if and only A-A

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

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Q: Let a and b be integers, at least one of them not 0. Prove that an integer e can be expressed as a…

A: Let a and b be intgers ateast one of them not 0. Our Aim is to prove that an integer e can be…

Q: -points of inflection (including both x and y values - you may use decimal approximations) -a sketch…

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Q: Prove that |ab|= |a | |b| for any numbers a and b.

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Q: Let a and d be integers. Prove that if d|(8a+7)and d|(5a+4), then d|3

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Q: Provide what is asked for. If an answer is not possible, write NONE. a ring R and a subring S of R…

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Q: Let a, b be nonzero integers. Prove that (a, b) = 1 if and only if (a + b, ab) = 1.

A: Given  Let a, b be nonzero integers  To Prove that gcd (a, b) = 1 if and only if gcd(a + b, ab) = 1…

Q: Proposition 1.43. A is the intersection of all closed subsets of X which con- tains A. Proof.…

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Q: Prove or disprove: if x is in set B and x > inf(B), then x/2  is in set B.

A: Let B= The set of natural number then  InfB=1 Let x=3 Since x∈B & x>infB.

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

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

Q: Prove or disprove. Let a, b, c ∈ Z. If a|c then ab|c

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Q: - Let T€ B(H). (a) Show that ker T'T=ker T. (b) Show that TT and TT have the same eigenvalues. (c)…

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Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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Q: Let x and y be integers. Prove that if x2 + y2 is odd, then x+y is odd

A: Given x and y be an integers. We have to prove that if x2+y2 is odd then x+y is odd. Since given…

Q: Let a, b € N. Choose all correct statements. O gcd(-a, b) = gcd(a, -b) O ged(2a – b, a + b) =…

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Q: Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

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Q: If a and b are even then GCD(a,b) must be 2

A: Given statement :- if a and b are even then GCD(a,b) must be 2

Q: Prove: If a, b and c≠0 are integers, then a|b if and only if ac|bc.

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Q: a and b are positive integers, show that gcd(a,b) = gcd(a,a+b).  Discrete math questio

A: To prove that gcd(a, b) = gcd(a, a + b) for positive integers a and b, you can use the properties of…

Q: SETS Prove that X ⊆ Y if and only if X ∪ Y = Y.

A: Draw a sets of X and Y and plot different cases and check all conditions having XUY=Y.

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: d = (a, b, c).

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Q: The_____ of A and B consists of all elements in either A or B or both.

A: The_____ of A and B consists of all elements in either A or B or both.   The answer of the above…

Q: Let A- and 8 I Find AB

A: Explanation of the answer is as follows

Q: Prove or disapprove that if a|bc, where a,b,c are positive integers and a≠0, then a|b or a|c

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Q: let A, B ⊂ R, and suppose A and B are closed. Prove that A ∩B is closed. Hint: You might try showing…

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Q: Prove T = { ... , −56, −42, −28, −14, 0, 14, 28, 42, ... } is a countable set

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Q: Prove by contradiction that for all integers a, b, and c, if a|b and a | c, then a |(b + c).

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Q: Let a, b e N. Choose all correct statements. O gcd(a, b) = gcd(-a, -b) O gcd(a, b) = gcd(a², b²) O…

A: We apply property of GCD to solve the problem

Q: Let A, B and C be sets. Use the algebra of sets to verify each statement. 1. A- (B U C) = (A – B) n…

A: Solution

Q: If A and B are sets such that ACB then A × BC B x B. true false

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Q: Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find B U (AN C). || {

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Q: 1) (AUB) x C = (A x C)U (B x C) 2) ASBAXCSBXC 3) (Ax B) n (C x D) (AnC) x (Bn D)

A: