Discrete Mathematics
Q272.
Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?Q273.
The number of onto functions (surjective functions) from set x={1,2,3,4} to set Y={a,b,c} is __________.Q275.
A partial order P is defined on the set of natural numbers as follows. Here \frac{x}{y} denotes integer division. i.(0, 0) \in P. ii.(a, b) \in P if and only if (a \% 10) \leq (b \% 10) and (\frac{a}{10},\frac{b}{10})\in P. Consider the following ordered pairs: i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153) Which of these ordered pairs of natural numbers are contained in P?Q278.
Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are:Q279.
If P, Q, R are subsets of the universal set U, then (P\cap Q\cap R)\cup (P^{C} \cap Q \cap R)\cup Q^{C} \cup R^{C} isQ280.
A set X can be represented by an array x[n] as follows x[i]=\left\{\begin{matrix} 1 &if i\in X \\ 0& otherwise \end{matrix}\right. Consider the following algorithm in which x,y and z are boolean arrays of size n; algorithm zzz(x[] , y[], z []) { int i; for (i=O; i < n; ++i) z[i] = (x[i] ^ ~y[i]) V (~x[i] ^ y[i]) } The set Z computed by the algorithm is