Let [n] denote the set of integers {1, 2, . , n). How many ways are there to permute the elements of the set [7] so that there is an even number in the first place?

Q: Show that some of the standard proper subsets of the real numbers are countable (e.g., N, Z, Q).

A: A set X is said to be a subset of a set Y if all the elements of the set X are contained in the set…

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

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

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Q: Compute for an arbitrary integer k

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Q: Z+ is the set of positive integers. Let A = {1,2,3), B = {n ∈ Z+ | n is even}, C = {n ∈ Z+ | n is…

A: concept Used: C∩D is the set  containing all elements of C that also in the set D C∪D is the set…

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: set N = {9, 43, 66}?

A: Given that  Set N = {9, 43, 66}   We know that  The subsets possible are null set , subset of size…

Q: {m belongs to all integers| m^2=3}    Now list the elements in the set?

A: The given set is {m belongs to all integers| m2=3}.To list down the elements in the given…

Q: How many positive integers less than 10000 are there which contain at least one 2 or at least one 3…

A: The objective is to evaluate the number of positive integers less that 10000 that contain at least…

Q: Find a set of four integers such that their order and the order of their absolute values are the…

A: We have to find a set of four integers such that their order and the the order of their absolute…

Q: Let A be the set of integers bigger than 3 and smaller than 10 and B the set of positive integers…

A: Solution-Let A be the set of integers bigger than 3 and smaller than 10.A={4,5,6,7,8,9}

Q: How many elements are in the set {2,2,2,2}

A: We have to find number of elements

Q: Let {\mathcal S}S be the set of all (nonnegative) 4-digit integers. How many integers does {…

A: Here given S is set of all (nonnegative) 4-digit integers We have to calculate,  How many 4 digits…