Discrete Mathematics Answers

List the members of these sets.

(a) {x | x is a real number such that x

2 = 5}

(b) {x | x is a positive integer less than 15}

(c) {x | x is the square of an integer and x < 200}

(d) {x | x is an integer such that x

2 = 5}

5. What is the probability that exactly eight 0 bits are generated when 10 bits are generated with the probability that a 0 bit generated is 0.9, the probability that a 1 bit generated is 0.1, and the bits are generated independently?

4. An unbiased coin is tossed twice. If A is the event: both head or tail have occurred and B is the event: at most one tail is observed find : i) P(A) ii) P(B) iii) P(A\B) iv) P(B\A)

Show that the explicit sequence {yn}∞n=0 such that yn = A(2n )+ B(-1)n for any nonzero

constants A and B is the solution of the recurrence relation

yn = yn-1 + 2yn-2 for n >1.

If you are at least 40 years old, a natural-born citizen of the Philippines, and you are a registered voter, then you are eligible to be elected as the Philippine  President. 

a: You are at least 40 years old. 

b: You are a natural-born citizen of the Philippines. 

r: You are a registered voter. 

e: You are eligible to be elected as the Philippine President. 

Prove that \sum_{i=0}^{n} 2^{i} = 2^{n + 1} - 1 Use mathematical induction for this proof and discuss/explain each step.

show that (A ∪ B)\C ⊆ A ∪ (B\C)

If A={1,2,3}, identify the power set of the given set A.

P(A)=

P(A)={ }

and

P(A)=

Prove that \sum_{i=0}^{n} 2^{i} = 2^{n + 1} - 1 Use mathematical induction for this proof and discuss/explain each step.