For each ne N, determine (with proof!) the number of subsets of the set [n] the sum of whose elements is odd. For example, for n = 2, there are 2 such subsets of [2], namely {1} (the sum of the elements is 1) and {1,2} (the sum of the elements is 3).

Q: . If n(A) = 15, n(B2)= 20, and n(A ∩ B) = 10,find n(A ∪ B)

A: Given: nA=15, nB=20, nA∩B=10

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: Show that 2N, the collection of all sets of natural numbers, is uncountable.

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Q: Find all integers 100 ≤ n ≤ 999 such that the last three digits of n² is same as n.

A: To find: All integers  such that the last three digits of is same as n.

Q: The diagram below shows ten circles joined by five lines with three circles Place all the…

A: Requirements: Numbers should range from 1 to 10.   Every line has three circles.   3. The amount for…

Q: Let n and k be natural numbers with n >k. how many subsets of {1,2, ..., 2n} have exactly k even…

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Q: d) Give a recursive definition of the sequence {a„}, n = 1, 2, 3... %3D n if a,= 2 + 1; and a15 e)…

A: d)  Here, given that an=2+1=3 So, for all n, an=3 which is the recursive definition.

Q: If a set S has n > 3 elements, how many subsets of S have more than one element, but less than n…

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Q: If A ∩ B = ∅ Find P(A) ∩ P(B)?] With all the steps

A: Power set of A is the set of all subsets of A Since it is given that A∩B=∅ which means there is no…

Q: In each of (a)-(f), answer the following questions: Is AS B? Is B C A? Is either A or B a proper…

A: As per the policy of bartleby the provisions is to solve only one 3 subparts of questions at a time

Q: Given 10 numbers a1, a2,.… , a10, from the set S natural numbers S = {1,2,3, ., 100} . Prove that…

A: Consider the set S=1, 2, 3, …, 100. Let a1, a2, …, a10 be 10 numbers from the set S. Take the set…

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

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Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

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Q: Prove: For all integers n, if (n + 1)2 is an even number, then n is an odd number. ii. Prove the…

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Q: Use the pigeonhole principle to prove that any 6-element subset of {1,2,..., 10} contains a pair of…

A: This question from discrete mathematics and topic is pigenhole principle.

Q: Prove that a selection of 7 numbers from the set {1, 2, . . . , 11} contains numbers m and n such…

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Q: (1.) Let T = {1, 2, 3, 4, 5, 6, 7, 8, 9}.  Suppose five integers are chosen from T. Show that it is…

A: 1) Let us choose a set = {1,2,3,4,5}  In this set, two maximum numbers are 4 and 5. Sum of 4 and 5…

Q: Determine all numbers n belong to N with the property that the set: A = {n, n + 1, n + 2, n + 3, n +…

A: SOLUTION:

Q: Let [n] denote the set of integers {1, 2, . , n). How many ways are there to permute the elements of…

A: Given that, The [n] denoted set of integers {1,2,..n} The numbers which are divisible by 2 are…

Q: Negate the statement: For all positive integers, n, there exists a positive integer, k, so that…

A: The negation of a statement is:- Statement:- p implies q. Negation:- p does not imply q.

Q: If one quarter of all 3-subsets of the integers 1, 2, ..., m contain the integer 5, determine m

A: This is a problem of counting.

Q: C. Think of a set with m + n elements as composed of two parts, one with m elements and the other…

A: m+n elements as composed of two parts.

Q: B. Let N be the set of natural numbers, A = {1, , , }, B = {:1<r <10, where a € N}. (10) State…

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Q: If S is the set of all positive integers greater that 19, is S finite or infinite?

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