Question

math question inside

Answer 1

is it that long

Answer 2

I just need someone to check this if right...and if wrong...please explain

p: You get an A on the final exam
q: You do every exercises in the book
r: You get an A in this class

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

a) You get an A in this class but you don;t do every exercise in the book => \(r \wedge \neg q\)
b) You get an A on final, you do every exercise in the book and you get an A in this class => \(p \wedge q \wedge r\)
c)To get an A in this class, it is necessary for you to get an A in the final \(r \leftrightarrow p\)
d) You get an A on the final, but you don't do every exercise in the book; nevertheless, you get an A on this class => \(p \wedge \neg q \wedge r\)
e) Getting an A on the final and doing every exercise in the book is sufficient for getting an A in this class => \((p \wedge q) \rightarrow r\)
f) You will get an A in this class if and only if you either do every exercise in the book or get an A in the final => \(r \leftrightarrow (q \vee p)\)

Answer 3

and yes @Jonask it was very long

Answer 4

i typed the whole question along with the latex so it took time

Answer 5

i would like questions like this where do you find them

Answer 6

i think b) is (p and q)implies r

Answer 7

why so? it just used "and"

Answer 8

and it's actually an e-book.. the title is Discrete Mathematics and its application 6th edition

Answer 9

sorry thats e) are you looking for solutions or smeting

Answer 10

my e) is (p and q) implies r

Answer 11

so does that mean i have no mistakes?

Answer 12

i am using the one by kenneth e rosen is that the1

Answer 13

this book is kenneth h. rosen...they could be different...

Answer 14

srry yes h

Answer 15

so do i have any mistakes?

Answer 16

i dont see ANY,I ALSO NEED SOME PRACTICE I JUST STARTED

Answer 17

hmm yeah..not much are good in these things... maybe @NewbieCarrot can give a second opinion

Answer 18

c) Should not be a bi-conditional. It is not saying that if you get an A on the final you then you will get an A in the class; however, it is saying that if you get an A in the class, then you did get an A on the final.

Answer 19

doesn't "it is necessary" mean that if and only if?

Answer 20

Nope.

Answer 21

"it is necessary and sufficient" means if and only if.

Answer 22

so it is necessary just means conditional?

Answer 23

Think about it. If I said "For rain, it is necessary to have clouds" then?

Answer 24

Does it mean that clouds imply rain?

Answer 25

hmmm....well my third choice that makes sense would be conjunction

Answer 26

It's not a bi-conditional.

Answer 27

It is a conditional, but just not two way.

Answer 28

so how do you write it out

Answer 29

\(r\rightarrow p\)

Answer 30

can i say then not p implies not r

Answer 31

no clouds no rain

Answer 32

Yeah, that is the contrapositive.