Math Answers

If x sin y =sin (p + y), p €R ,show that sin(p)dy/de sin^2y=0

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

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 don’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.

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.

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.

2. Conditional equivalence. Which of the following implications are true?
a) If 2 + 2 = 5 then 2 + 2 = 6.
b) If 2 + 2 = 4 then the world is flat.
c) If both of the previous statements are true then 2 + 2 = 7.

Q1. Propositions. Which of the following sentences are propositions?
a) It rained yesterday.
b) The last digit of the smallest prime number larger than 100100 is 1.
c) This sentence is false.
d) 6 + 5 = 10.

What is lattitude and longitude?

prove that nCr+1=nCr (n-r/r+1)