Letp,qandrbe the propositions such that,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 the following propositions usingp,q,rand logical connectives.
(a) If you do every exercise in this book then you will get an A in this class.
(b) You get an A in class only if you get an A in the final exam.
(c) To get an A in this class it is necessary for you to get an A in the final.
(d) Getting an A in the final and doing every exercise in this book is sufficient for getting anA in this class.
(e) You will get an A in this class if and only if you either do every exercise in this book oryou get an A on the final exam.
(a) If you do every exercise in this book then you will get an A in this class.
(b) You get an A in class only if you get an A in the final exam.
(c) To get an A in this class it is necessary for you to get an A in the final.
(d) Getting an A in the final and doing every exercise in this book is sufficient for getting anA in this class.
(e) You will get an A in this class if and only if you either do every exercise in this book oryou get an A on the final exam.
1 answer:
Answer:
a) r→q
b) r→p
c) r→p
d) r→ p∧q
e) r→ p∨q
Step-by-step explanation:
Using logical connectives, as shown in the picture below, we can write all of the statements of the question.
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"
a) r→q
b) r→p
c) r→p
d) r→ p∧q
e) r→ p∨q
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The probability that, at the tip of the fourth round, each of the players has four coins is 5/192.
Given that game consists of 4 rounds and every round, four balls are placed in an urn one green, one red, and two white.
It amounts to filling in an exceedingly 4×4 matrix. Columns C₁-C₄ are random draws each round; row of every player.
Also, let be the quantity of nonzero elements in
Let .
Parity demands that and
must equal 2 or 4.
Case 1: =4 and
=4. There are
=3 ways to put 2-1's in
, so there are 3 ways.
Case 2: =2 and
=4. There are 3 ways to position the -1 in
, 2 ways to put the remaining -1 in
(just don't put it under the -1 on top of it!), and a pair of ways for one among the opposite two players to draw the green ball. (We know it's green because Bernardo drew the red one.) we are able to just double to hide the case of
for a complete of 24 ways.
Case 3: . There are 3 ways to put the -1 in
. Now, there are two cases on what happens next.
- The 1 in
goes directly under the -1 in
. There's obviously 1 way for that to happen. Then, there are 2 ways to permute the 2 pairs of 1,-1 in
and
. (Either the 1 comes first in
- The 1 in
Hence, there are 3(2+2×2)=18 ways for this case. There's a grand total of 45 ways for this to happen, together with 12³ total cases. The probability we're soliciting for is thus 45/(12³)=5/192
Hence, at the top of the fourth round, each of the players has four coins probability is 5/192.
Learn more about probability and combination is brainly.com/question/3435109
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