Discrete Mathematics
Q261.
Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements: I. Each compound in U \ S reacts with an odd number of compounds. II. At least one compound in U \ S reacts with an odd number of compounds. III. Each compound in U n S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE?Q262.
A function f:\mathbb{N}^{+}\rightarrow \mathbb{N}^{+}, defined on the set of positive integers \mathbb{N}^{+}, satisfies the following properties: f(n)=f(n/2) if n is even f(n)=f(n+5) if n is odd Let R={i|\exists j:f(j)=i} be the set of distinct values that f takes. The maximum possible size of R is ____.Q263.
Let N be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to N R: Set of functions from N to {0, 1} S: Set of finite subsets of N. Which of the sets above are countable?Q264.
Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible functions defined from X to Y. Let f be randomly chosen from F. The probability of f being one-to-one is ________.Q265.
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?Q267.
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}Q268.
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?