Let X be an infinite set, then any topology on X is also infinite. Select one: O True O False

Q: Suppose A and B are subsets of a universal set U. Don't use Venn Diagrams to Show that…

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

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Q: Let A and B be sets. Prove that the intersection of A and B is is a subset of the union between A…

A: To show that the elements which are common to both A and B belong to either A or B.

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: Prove T = { ... , −56, −42, −28, −14, 0, 14, 28, 42, ... } is a countable set

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Q: Write the set {x : x is a positive integer and x2< 40} in the roster form.

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Q: show that empty set, X is an element of S intersection T in topology

A: Here We have to show that empty set must be in S∩T where S and T are topology on set X.

Q: Let A and B be sets. Prove that A – B = AU B.

A: Let A and B be two sets. Now, A¯-B=A¯∩B¯ ⇒A¯-B=A∪B¯  by De Morgan's Law