ICS253_081_Major2

# ICS253_081_Major2 - Neatness is close to Godliness ICS 253...

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ICS 253 : Discrete Structures 1 Adel F. Ahmed January 18, 2009(081) St.Name: St.Number: Major 2 Time: 120 minutes Question 1: Answer the following: [2 points each] If f : R R and f ( x ) = x 2 + 1. Is f a bijection? How many strings are there of lowercase letters of length four or less? Is f g = g f ? Question Max Pts Points 1 28 2 12 Total 40 If the successor of a set A is defined as A ∪ { A } . Then find the successor of {∅ , {∅}} . What is the coefficient of x 8 y 9 in the expansion of (3 x + 2 y ) 17 ? How many positive integers not exceeding 100 are divisible either by 4 or by 6? Translate the quantification x Z ( x 2 > 0) into English. How many positive integers between 100 and 999 inclusive are divisible by 3 or 4? Find the truth set of P ( x ) : “ x 2 > x ”. Find f g where f ( x ) = x 2 + 1 and g ( x ) = x + 2. (show steps). How many bit strings of length 10 over the alphabet { a, b, c } have either exactly three a s or exactly four b s? Let F be the function such that F ( n ) is the sum of the first n positive integers. Give a recursive definition of F

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