Set Theory


Q41.

Suppose U is the power set of the set S={1,2,3,4,5,6}. For any T\inU, let |T| denote the number of elements in T and T' denote the complement of T. For any T,R\inU, let T\R be the set of all elements in T which are not in R. Which one of the following is true?
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Q42.

The cardinality of the power set of { 0, 1, 2,..., 10 } is _________.
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Q43.

For a set A, the power set of A is denoted by 2^{A}. If A={5,{6},{7}}, which of the following options are TRUE? I. \phi \in 2^{A} II. \phi \subseteq 2^{A} III. {5,{6}} \in 2^{A} IV. {5,{6}}\subseteq 2^{A}
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Q44.

Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U\ltV if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements: S1: There is a subset of S that is larger than every other subset. S2: There is a subset of S that is smaller than every other subset. Which one of the following is CORRECT?
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Q45.

Which one of the following is true?
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Q46.

The number of elements in the power set of the set {{A, B}, C} is
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Q47.

The symmetric difference of sets A={1,2,3,4,5,6,7,8} and B={1,3,5,6,7,8,9} is:
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Q48.

Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?
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Q49.

The number of onto functions (surjective functions) from set x={1,2,3,4} to set Y={a,b,c} is __________.
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