Let S={1,2,3,4,5,6} How many subsets are there of cardinality 4?

Q: Let S={1,2,3,4,5,6,7,8,9} How many subsets of cardinality 6 have {2,3,5} as a subset?

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Q: Prove that each of the following pairs of sets have the same cardinality. (a) We have the sets X and…

A: In set theory, one important concept is that of cardinality, which is the measure of the "size" of a…

Q: Which of the following sets are closed under multiplication? 11. (i) X = {1, 2, 3, 4, ..., 30} (ii)…

A: i) If we multiply 30 and 2 from set X, then we get 30*2= 60  This is not in the set. So, X is not…

Q: Use definition of set X has the same cardinality as set Y prove that Card(R = {2}) = Card(R – {0}).

A: We know thatTwo sets X and Y have the same cardinality if there exists a bijection (i.e one-to-one…