Show that a set S has infinite elements if and only if it has a subset...

Show that a set S has infinite elements if and only if it has a subset U such that (1) U does not equal to S and (2) U and S have the same cardinality.

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Colby Messinger answered 3 months ago

i)Show that infinite decidable language has infinite decidable subset ? ii)Show that any infinite decidable language...

i)Show that infinite decidable language has infinite decidable subset ? ii)Show that any infinite decidable language L has an infinite decidable subset J with the property that L − J is also infinite. iii. Does the statement in part i of this problem still true if L is only recognizable ? Show or Counter example. No Spam please.

Prove that a subset of a countably infinite set is finite or countably infinite

Let A be an infinite set and let B ⊆ A be a subset. Prove: (a)...

Let A be an infinite set and let B ⊆ A be a subset. Prove: (a) Assume A has a denumerable subset, show that A is equivalent to a proper subset of A. (b) Show that if A is denumerable and B is infinite then B is equivalent to A.

Show that a subset of R is open if an only if it can be expressed...

Show that a subset of R is open if an only if it can be expressed as a union of open intervals

Let S be a set and P be a property of the elements of the set,...

Let S be a set and P be a property of the elements of the set, such that each element either has property P or not. For example, maybe S is the set of your classmates, and P is "likes Japanese food." Then if s ∈ S is a classmate, he/she either likes Japanese food (so s has property P) or does not (so s does not have property P). Suppose Pr(s has property P) = p for a uniformly...

Let S be a subset of a vector space V . Show that span(S) = span(span(S))....

Let S be a subset of a vector space V . Show that span(S) = span(span(S)). Show that span(S) is the unique smallest linear subspace of V containing S as a subset, and that it is the intersection of all subspaces of V that contain S as a subset.

Show that there are only two distinct groups with four elements, as follows. Call the elements...

Show that there are only two distinct groups with four elements, as follows. Call the elements of the group e, a. b,c. Let a denote a nonidentity element whose square is the identity. The row and column labeled by e are known. Show that the row labeled by a is determined by the requirement that each group element must appear exactly once in each row and column; similarly, the column labeled by a is determined. There are now four table...

1)Show that a subset of a countable set is also countable. 2) Let P(n) be the...

1)Show that a subset of a countable set is also countable. 2) Let P(n) be the statement that 13 + 23 +· · ·+n3 =(n(n + 1)/2)2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis....

Show that the language F={M| M is a Turing machine , and L(M) contains infinite elements}...

Show that the language F={M| M is a Turing machine , and L(M) contains infinite elements} is not Turing recognizable.

The subset-sum problem is defined as follows. Given a set of n positive integers, S =...

The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1, a2, a3, ..., an} and positive integer W, is there a subset of S whose elements sum to W? Design a dynamic program to solve the problem. (Hint: uses a 2-dimensional Boolean array X, with n rows and W+1 columns, i.e., X[i, j] = 1,1 <= i <= n, 0 <= j <= W, if and only if there is a subset of...

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