Set Theory
Q12.
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?Q13.
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}Q16.
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?Q18.
Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?Q19.
The number of onto functions (surjective functions) from set x={1,2,3,4} to set Y={a,b,c} is __________.