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Draw the venn diagram of sets A, B and C where A is contained in (subset equal to) B , A intersection B doesn't equal to phi (empty set) , B intersection C = phi ( empty set) . What is the universal set you have chosen? Justify your choice of sets in the diagram?

Suppose we model the spread of a virus in a certain population as follows. On day 1, one person is infected. On each subsequent day, each infected person gives the cold to two others.

(a) Write down a recurrence relation for this model.

(b) What are some of the limitations of this model? How does it fail to be realistic?

(a) Write down a recurrence relation for this model.

(b) What are some of the limitations of this model? How does it fail to be realistic?

Which of the following statement are True.(1) x>0 is necessary for x+2>1?

Problem of recursion (Discrete Math)

Assume that changing the temperature of an object during a time interval is proportional to the difference in temperature between the object and the environment. A piece of metal, originally at 1000 degrees farenheight is cooled to 250 degrees farenheight in 5 hours in a medium temperature of 70 degrees farenheight. When will it reach a temperature of 250 degrees farenheight?

{ T(t)=1000 ; t=1

T(t) = { T(t-1)+r[S-T(t-1) ] ; t>1

Where S is the temperature of the medium and r = k.

Assume that changing the temperature of an object during a time interval is proportional to the difference in temperature between the object and the environment. A piece of metal, originally at 1000 degrees farenheight is cooled to 250 degrees farenheight in 5 hours in a medium temperature of 70 degrees farenheight. When will it reach a temperature of 250 degrees farenheight?

{ T(t)=1000 ; t=1

T(t) = { T(t-1)+r[S-T(t-1) ] ; t>1

Where S is the temperature of the medium and r = k.

Q : Determine whether these biconditionals are true or false.

a) 2 + 2 = 4 if and only if 1 + 1 = 2.

b) 1 + 1 = 2 if and only if 2 + 3 = 4.

c) 1 + 1 = 3 if and only if monkeys can fly.

d) 0 > 1 if and only if 2 > 1

a) 2 + 2 = 4 if and only if 1 + 1 = 2.

b) 1 + 1 = 2 if and only if 2 + 3 = 4.

c) 1 + 1 = 3 if and only if monkeys can fly.

d) 0 > 1 if and only if 2 > 1

Let p, q, and r be the propositions

p : You get an A on the final exam.

q : You do every exercise in this book.

r : You get an A in this class.

Write these propositions using p, q, and r and logical connectives (including

negations).

a) You get an A in this class, but you do not do every exercise in this book.

b) You get an A on the final, you do every exercise in this book, and you get an A in

this class.

c) To get an A in this class, it is necessary for you to get an A on the final.

d) You get an A on the final, but you donâ€™t do every exercise in this book;

nevertheless, you get an A in this class.

e) Getting an A on the final and doing every exercise in this book is sufficient for

getting an A in this class.

f) You will get an A in this class if and only if you either do every exercise in this

book or you get an A on the final.

p : You get an A on the final exam.

q : You do every exercise in this book.

r : You get an A in this class.

Write these propositions using p, q, and r and logical connectives (including

negations).

a) You get an A in this class, but you do not do every exercise in this book.

b) You get an A on the final, you do every exercise in this book, and you get an A in

this class.

c) To get an A in this class, it is necessary for you to get an A on the final.

d) You get an A on the final, but you donâ€™t do every exercise in this book;

nevertheless, you get an A in this class.

e) Getting an A on the final and doing every exercise in this book is sufficient for

getting an A in this class.

f) You will get an A in this class if and only if you either do every exercise in this

book or you get an A on the final.

Q : Let p and q be the propositions

p : You drive over 65 miles per hour.

q : You get a speeding ticket.

Write these propositions using p and q and logical connectives (including

negations).

a) You do not drive over 65 miles per hour.

b) You drive over 65 miles per hour, but you do not get a speeding ticket.

c) You will get a speeding ticket if you drive over 65 miles per hour.

d) If you do not drive over 65 miles per hour, then you will not get a speeding ticket.

e) Driving over 65 miles per hour is sufficient for getting a speeding ticket.

f) You get a speeding ticket, but you do not drive over 65 miles per hour.

g) Whenever you get a speeding ticket, you are driving over 65 miles per hour.

p : You drive over 65 miles per hour.

q : You get a speeding ticket.

Write these propositions using p and q and logical connectives (including

negations).

a) You do not drive over 65 miles per hour.

b) You drive over 65 miles per hour, but you do not get a speeding ticket.

c) You will get a speeding ticket if you drive over 65 miles per hour.

d) If you do not drive over 65 miles per hour, then you will not get a speeding ticket.

e) Driving over 65 miles per hour is sufficient for getting a speeding ticket.

f) You get a speeding ticket, but you do not drive over 65 miles per hour.

g) Whenever you get a speeding ticket, you are driving over 65 miles per hour.

Q : Let p and q be the propositions

p : It is below freezing.

q : It is snowing.

Write these propositions using p and q and logical connectives (including

negations).

a) It is below freezing and snowing.

b) It is below freezing but not snowing.

c) It is not below freezing and it is not snowing.

d) It is either snowing or below freezing (or both).

e) If it is below freezing, it is also snowing.

f) Either it is below freezing or it is snowing, but it is not snowing if it is below freezing.

g) That it is below freezing is necessary and sufficient for it to be snowing.

p : It is below freezing.

q : It is snowing.

Write these propositions using p and q and logical connectives (including

negations).

a) It is below freezing and snowing.

b) It is below freezing but not snowing.

c) It is not below freezing and it is not snowing.

d) It is either snowing or below freezing (or both).

e) If it is below freezing, it is also snowing.

f) Either it is below freezing or it is snowing, but it is not snowing if it is below freezing.

g) That it is below freezing is necessary and sufficient for it to be snowing.

Q : Suppose that during the most recent fiscal year, the annual revenue of Acme

Computer was 138 billion dollars and its net profit was 8 billion dollars, the

annual revenue of Nadir Software was 87 billion dollars and its net profit was 5

billion dollars, and the annual revenue of Quixote Media was 111 billion dollars

and its net profit was 13 billion dollars. Determine the truth value of each of

these propositions for the most recent fiscal year.

a) Quixote Media had the largest annual revenue.

b) Nadir Software had the lowest net profit and Acme Computer had the largest

annual revenue.

c) Acme Computer had the largest net profit or Quixote Media had the largest net

profit.

d) If Quixote Media had the smallest net profit, then Acme Computer had the largest

annual revenue.

e) Nadir Software had the smallest net profit if and only if Acme Computer had the

largest annual revenue.

Computer was 138 billion dollars and its net profit was 8 billion dollars, the

annual revenue of Nadir Software was 87 billion dollars and its net profit was 5

billion dollars, and the annual revenue of Quixote Media was 111 billion dollars

and its net profit was 13 billion dollars. Determine the truth value of each of

these propositions for the most recent fiscal year.

a) Quixote Media had the largest annual revenue.

b) Nadir Software had the lowest net profit and Acme Computer had the largest

annual revenue.

c) Acme Computer had the largest net profit or Quixote Media had the largest net

profit.

d) If Quixote Media had the smallest net profit, then Acme Computer had the largest

annual revenue.

e) Nadir Software had the smallest net profit if and only if Acme Computer had the

largest annual revenue.

Suppose that SmartphoneA has 256 MB RAM and 32 GB ROM, and the resolution

of its camera is 8 MP; Smartphone B has 288 MB RAM and 64 GB ROM, and the

resolution of its camera is 4 MP; and Smartphone C has 128 MB RAM and 32 GB

ROM, and the resolution of its camera is 5 MP. Determine the truth value of each

of these propositions.

a) Smartphone B has the most RAM of these three smartphones.

b) Smartphone C has more ROM or a higher resolution camera than Smartphone B.

c) Smartphone B has more RAM, more ROM, and a higher resolution camera than

Smartphone A.

d) If Smartphone B has more RAM and more ROM than Smartphone C, then it also

has a higher resolution camera.

e) Smartphone A has more RAM than Smartphone B if and only if Smartphone B has

more RAM than Smartphone A.

of its camera is 8 MP; Smartphone B has 288 MB RAM and 64 GB ROM, and the

resolution of its camera is 4 MP; and Smartphone C has 128 MB RAM and 32 GB

ROM, and the resolution of its camera is 5 MP. Determine the truth value of each

of these propositions.

a) Smartphone B has the most RAM of these three smartphones.

b) Smartphone C has more ROM or a higher resolution camera than Smartphone B.

c) Smartphone B has more RAM, more ROM, and a higher resolution camera than

Smartphone A.

d) If Smartphone B has more RAM and more ROM than Smartphone C, then it also

has a higher resolution camera.

e) Smartphone A has more RAM than Smartphone B if and only if Smartphone B has

more RAM than Smartphone A.