prove that any set S subset of {1,2,,...100} with |S|=26 contains at least one odd number or it contains two numbers, x different from y, for which y is divisible by x

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: List the first four elements of the set { x | x = 4k + 1, and k is a natural number}  (List each…

A: Given set { x | x = 4k + 1, and k is a natural number} = {4×1+1, 4×2+1, 4×3+1, 4×4+1, ... } = {5, 9,…

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

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Q: 2. a. List all 3-combinations for the set {x1, x2, x3, X4, Xs}. Deduce the value of (,). b. List all…

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Q: 1. A₁-[0,4], A2-[1,5), A3= [0.5,3], A4- (1,9] As 2. A₁-[0,4], A₂-[1,5), A3- [0.5,3], A- (1,9] As 3.…

A: Given- Ω=set of all real numbers  A= index set  To identify the generalized union and intersection…

Q: create all the subsets of B= {2,3,5,7,11} and place it in a power set

A: The objective of this question is to create all possible subsets of the set B= {2,3,5,7,11} and…

Q: Pzif akb then [a,b]-(- All of a,b are in real numbers

A: The given statements are: p: a<b q: a, b=(-∞, b] \ -∞, a Prove: If p, then q. If a<b, then  a,…

Q: list all the subsets of  {1,2,∅}   and {{R}} R= real number

A: Number of subsets of a set with n elements is 2^n

Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

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: b. How many elements are in the set {a, {a, b}, {a} }? C. For each positive integer x, let A1` =…

A: Use the definition of set and its elements to solve this problem as in next step.

Q: Prove that the set Q \ Z is countable.

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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: 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: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: II. Let Q-set of all real numbers, A-index set. Identify the generalized union and intersection of…

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Q: Show that the set W of all whole numbers, W = {0, 1, 2, 3, . . 3, and N = 11, 2, 3, 4, . . 3 are…

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

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Q: Let a1, a2, a3, . .., an be real numbers. Prove that at least one of them is greater than the…

A: We prove it by contradiction.

Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: Q.No.2 Let X be a universal set and A, B be the subsets of X.Then prove the following. (a) ((A*…

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Q: Use sets U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 3, 7, 8), and B = {3, 4, 5, 6, 7, 9, 10) to…

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Q: 1. Show that 2 is a primitive root modulo 13. 2. For each element a in T, find the index of a mod 13…

A: T=1,2,3,4,5,6,7,8,9,10,11,12

Q: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

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Q: set of integers is denoted by Z

A: There is some standard notation for certain types of sets . Set of real numbers is denoted by R,…

Q: Show that S has 2n subsets.

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