Discrete Mathematics Answers

Translate the gaming system requirement, , into English where the predicate S(x,y) is “x is in state y” and where the domain for x and y consists of all systems and all possible states, respectively.

Express this gaming system requirement using predicates, quantifiers, and logical connectives: “When there are less than 2 gigabytes of available RAM, an error message is displayed.”

1. There is a smallest positive integer.

2. There is no smallest positive real number.

3. There exists an integer that is larger than the product of any two 

    integers.

4. Every pair of integers has a common divisor.

1. There is a smallest positive integer.

1.   The sequence {Un} is defined by the first term u1=-2 and the recurrent relation : Un+1=Un/4 +3

a.   Evaluate U2,U3,U4

b.    Consider  the sequence Vn such that Vn=Un+1-Un for n>=2

c.    Prove that {Vn} is a G.P 

d.   Express Vn  and Un  in terms of n.

e.     Evaluate the limits of  Un and Vn  

f.    Is Un an increasing  or decreasing sequence ? 

If 20 candidates appear in a competitive exam. Then show that there exist at least 2 students among them whose roll number differ by a multiple of 19.