18. Prove that if B C A, A is infinite, and B is finite, then A \ B is infinite.

Q: Prove the following set infinite: {5,9,13,17,...}

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Q: Decide with a proof that the set Nk is countable or not, where N is the set of natural numbers and k…

A: According to the given information it is required to proof that the set

Q: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

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Q: 6. Prove that if gcd(a , b) = 1, then gcd(a + b, ab) = 1.

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A: As per honor code, we are entitled to solve only 1 question at a time so I am providing the same.…

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Q: Assume that A and B are in NP. Show A n B that is also in NP.

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Q: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

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Q: If a,b,c,d are in continued properties,prove that

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Q: O Show that if A is finite, then P (A) is finite.

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Q: 7. Suppose A and B are sets and A is finite. Prove that A ~ B iff B is also finite and |A| = |B|.

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Q: discrete

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Q: 26. Let I be the set of all infinite sets. Is I an element of itself?

A: Given I is the set of all infinite sets.  We check whether I is an element of itself.

Q: Suppose B C A, B + A, and B ~ A. Prove that A is infinite.

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Q: 4. Is the set Q² x {a,b,c} countable or uncountable? You must justify your answer with a proof.

A: Given : ℚ2×a , b ,c  To Prove : ℚ2×a , b ,c  countable or uncountable

Q: 4 Prove that סלא is Riomonn inkgpable

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Q: Suppose a set A is uncountably infinite, that U is countably infinite, and that UC A. Show that A -…

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Q: 3 10. Show that R² span

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Q: Prove or disprove: If A ⊆ B ⊆ C and A and C are countably infinite, then B is countably infinite.

A: Let A ⊆ B ⊆ C The sets A is countably infinite. Since A ⊆ B and A is countably infinite, it implies…

Q: 2. (i) Show that given finitely many countable sets A1, A2, , An, the set A1 x A2 x .. x An is also…

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Q: 9. Give a proof by contradiction to show if A and B are sets, then A N (BN A') = {}.

A: Suppose A and B are sets.

Q: 11. Use set identities or different proof method to show that: a) (B- A)U(C- A) = (BUC)- A b) (4 –…

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Q: 4 A school has 137 math students. a) Prove that if the principal hires 8 math teachers, then at…

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Q: 4. Let b > a > 0. Show that (a,b] is neither closed nor open.

A: Explanation of the solution is given below....

Q: Prove that ord,(a + b) > min(ord,a, ord,b) with equality holds if ord,a ± ord,b.

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Q: 12. Prove: If AC B and C C D, then ANCCBND.

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Q: 1. Prove with the resolution calculus -(PA-Q) -P (RAS) VQ

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Q: 5.3.8 Prove that if A CR is a finite set, then A is well-ordered.

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Q: 3. Suppose a, b, c E Z. Prove that if a? + b = c²,, then a is even or b is even.

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Q: 2. If the set S in each part is finite, write down S. i. S={primes) ii. S= (even primes) iii. S=…

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Q: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

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Q: Consider the set A = {xy : x ∈ N, y ∈ N} = {1, 2, 22, 23, 24, ...., 3, 32, 33, 34,......, 4, 42, 43,…

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Q: 1. It consists of elements that are in A but not in B. universa

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Q: (3.2) Indicate which of the following sets are compact in X. (a) C = {4,n € N}, X = R (b) C = Qn (0,…

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Q: (1) Disprove the statement "For all integers a, b if a | b2 and a < b then a | b." by giving a…

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Q: Remark. Every (finite Countable set is negligible or infinite)

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Q: 14.2 Limits A fxn is continvous if

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Q: Let A be uncountable and B be countable. Prove that A\B is uncountable.

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Q: Prove in any Pythagorean triple (a, b, c) that either a or b is divisible by 3 and one of a, b, c is…

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Q: Show that if A is a countable set, and B CA is infinite, then B is countable. [Hint: How could we…

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Q: Suppose that a,beG such that a = m and b =n with Gcd (m,n) = 1. Then n | is in mn

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Q: 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded…

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