Cardinality

Let A and B be non-empty finite sets such that there exist one-to-one and onto functions (i) from A to B and (ii) from A × A to A U B. The number of possible values of |A| is _____...

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$. The number of possible va...

Consider the following two statements about regular languages: S 1 : Every infinite regular language contains an undecidable language as a subset. S 2 : Every finite language is re...

In an Entity-Relationship $$(ER)$$ model, suppose $$R$$ is a many-to-one relationship from entity set $$E1$$ to entity set $$E2.$$ Assume that $$E1$$ and $$E2$$ participate totally...

The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$$ is _____________.

Consider the join of a relation R with a relation S. If R has m tuples and S has n tuples then the maximum and minimum sizes of the join respectively are

Suppose $$X$$ and $$Y$$ are sets and $$\left| X \right|$$ and $$\left| Y \right|$$ are their respective cardinalities. It is given that there are exactly 97 functions from $$X$$ to...

The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is

Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is

Let $$S$$ be an infinite set and $${S_1},\,\,{S_2},....\,\,{S_n}$$ be sets such that $${S_1} \cup {S_2} \cup ....... \cup {S_n} = S$$. Then