q → r) and q → (p ∨ r).
Q2. Write the converse, inverse and contrapositive of the statement:
“I will score marks whenever I will study”.
Q3. Convert the following compound propositions into English sentences for given
p: It is below freezing.
q: It is snowing.
(i) ¬q → ¬p
(ii) ¬q ∨ (¬p ∧ q )
(iii) p ↔ ¬q
(iv) p ∨ q
(v) ¬q ∧ ¬p
Q4. Determine whether each of the statements is true or false.
(i) If 1 + 1 = 2, then 2 + 2 = 5.
(ii) If 1 + 1 = 3, then 2 + 2 = 4.
(iii) If 1 + 1 = 3, then dogs can fly.
(iv) Monkeys can fly if and only if 1 + 1 = 3.
(v) A number is prime if and only if it is divisible by 1 and itself.
The two point source interference pattern is set up in a ripple tank such that the wavelength of the waves is 5.0cm. Point P is chosen such that it is on the second nodal line and closer to S1. When waves from S1 and S2 meet at point P, how much further did the waves from S2 travel than the waves from S1
"Let A, B, C, D be points in this order on the line g and let P be a point in the plane that is not on g."
Show, if the inequality |AP|+|DP|>|BP|+|CP| holds for all points P that do not lie on g, that |AB|=|CD|"
I appreciate all ideas or solutions :)
and how to solve:
“A history lecture hall class has 15 students. There is a 15% absentee rate per class meeting. Find the probability that exactly one student will be absent from class.”
I already know that:
n = 15
p = 15%
q = 1 - 15 = 1 - 0.15 = 0.85
...and then you do: p (x = 1) = C 15 & 1 and then...
Please help me understand the rest. Thank you!
et loans (he doesn't "earn" income). With the loans (L) he needs to decide between first period consumption (C1) and investment (I). The amount invested will allow him to get a second period income Y with probability P which is increasing in I (therefore, P(I)), In case of success and the person obtain Y, the individual should use Y to repay the loan (L) that he requested in the first period and consume in the second period (C2). However, with probability 1 - P(I), the person don't get Y and therefore only consume C1. Note that if the individual only invest the loan (L=I) and don't obtain Y, he can't consume anything. That motivates him not to invest the whole loan and keep part of the loan in order to warrant at least first period consumption. Therefore, considering B the parameter for the time preference, the problem would be:
max U=ln(C1) + Bln(C2)
s.t: L = I + C1
Y(I) = L(1+r) + C2
with Probability P(I)
s.t: L = I + C1
with probability 1 - P(I)
My question is, Have you ever seen something like this? If yes, how to proceed? What is more important, I really need a bibliography (a book or article talking about this)