Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Here a function f: S -> T is a mapping between two sets, called the domain and range. An onto function, also known as a
surjective function, is a function where every element in the range set is mapped to by at least one element in the domain
set. In other words, every element in the range has a pre-image in the domain. In this case, the domain set S is defined as
{1,2,3,....,10} and the range set T is defined as {11,12,13,....,20}.
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- 1. Big-O Notation Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. We say that f ( x ) is O ( g ( x ) ), read as "f ( x ) is big-oh of g ( x )", if there are constants C and k such that | f ( x ) | ≤ C | g ( x ) | whenever x > k. (a) Show that f(x) = x2 + 2x + 1 is O(x2) Solution: When x>1; ? 2 (1 + 2 ? + 1 ? 2 ) < ? 2 (1 + 2 1 + 1 1 2 ) = 4? 2 So, ??? ? > 1, ? 2 + 2? + 1 < 4? 2 From the definition 0 ≤ f(x) ≤ cg(x) for x≥1 Hence, for N0 = 1; c=4; and g(x)=x2 for N0 = 2; c=3; and g(x)=x2 for N0 = 3; c=2; and g(x)=x2 … Therefore, ? ? + ?? + ? = ?(? ? ) O(g(x)) = {f(x)|there exist positive constant c and N0 such that 0 ≤ f(x) ≤ cg(x) for all x≥N0} 2. Show that 7x2 is O(x3). 3. Suppose there are x number of boxes to be delivered to x number of household that is 2km apart, what is the distance travelled by the transport delivery service? 4. In number 3, suppose that each boxes…arrow_forwardplease help me quickly solve it all I need your help nessery please help mearrow_forward4.Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) a)Find all many keys for Rarrow_forward
- XOR function mappings can easily be classified by decision trees. True Falsearrow_forwardcountability of the set of functions that map positive integers to {0,1}arrow_forwardQuestion 7 The function f(x)=x2 from set of positive real numbers to positive real numbers is not injective not surjective both injective and surjective Neither injective nor surjectivearrow_forward
- 5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.arrow_forwardLet f be the function from {p,q,r,s,t} to {3, 4, 5, 6} defined by f(p) = 6, f(q) = 3, f(r) = 4, f(s) = 5 and f(t)=6. (In order to get full credit you have to explain why) i. Is f an onto function? if so why? ii. is fa one-to-one function? if so why? iii. is function f is "one-to-one correspondence"? if so why?arrow_forwardDetermine whether each of the following functions f : {a,b,c,d} -> {a,b,c,d} is one-to-one and/or onto. (a) f(a) = b, f(b) = a, f(c) = b, f(d) = c (b) f(a) = b, f(b) = b, f(c) = d, f(d) = c (c) f(a) = b, f(b) = a, f(c) = c, f(d) = d (d) f(a) = d, f(b) = a, f(c) = c, f(d) = b (e) f(a) = c, f(b) = d, f(c) = aarrow_forward
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