Question

Consider the following statements:
P: The integer n is divisible by 2
Q. The integer n is divisible by 3
R. The integer n is divisible by 6

Translate the following logical expressions into good English sentences.
1. ~P V ~Q
2. [(P V Q) ^ ~(P ^Q)] -> ~R

Answer 1

so ~P would be that the integer n isn't divisible by 2 and ~Q would be that the integer n isn't divisible by 3
Therefore, ~P V ~Q would mean that the integer n isn't divisible by 2 or the integer n isn't divisible by 3

Answer 2

yes

Answer 3

second is kind of nasty... so I'll break it into parts
P V Q = > The integer n is divisible by 2 or The integer n is divisible by 3
P ^ Q = > The integer n is divisible by 2 or The integer n is divisible by 3
~(P ^ Q) = > The integer n isn't divisible by 2 or The integer n isn't divisible by 3

implies not R which is The integer n isn't divisible by 6

Answer 4

A HA!
If The integer n is divisible by 2 or The integer n is divisible by 3 AND The integer n isn't divisible by 2 AND The integer n isn't divisible by 3 then the integer n isn't divisible by 6

Answer 5

OOPS! ^ IS AND! OUCH
P ^ Q = > The integer n is divisible by 2 and The integer n is divisible by 3 ~(P ^ Q) = > The integer n isn't divisible by 2 and The integer n isn't divisible by 3

Answer 6

that is so wordy...

Answer 7

this whole sentence is nasty
:/
If The integer n is divisible by 2 or The integer n is divisible by 3 AND The integer n isn't divisible by 2 AND The integer n isn't divisible by 3 then the integer n isn't divisible by 6

Answer 8

how can we make this sentence less messy?

Answer 9

If the integer n is either divisible by 2 OR 3, and if it isn't divisible by 2 AND 3, then the integer n isn't divisible by 6

Answer 10

What logical expression conveys the meaning of the following English sentence?
An integer n is divisible by 6 if and only if it is divisible by both 2 and 3.
R <---> (P ^ Q)

Answer 11

looks good

Answer 12

Write the contra-positive of [(P V Q) ^ ~(P ^Q)] -> ~R
eeeeeyah let [(P V Q) ^ ~(P ^Q)] be J since it's so long
J --- > ~R
converse
~R --->J
contrap
R ---> J

Answer 13

J --- > ~R
converse
~R --->J
contrap
R ---> ~J

Answer 14

oh crud X>X my bad... tired hands lol

Answer 15

but yes it would be regular r and not J
R ---> ~J

Answer 16

no need to simplify right ? just writing it is enough ?

Answer 17

yup ^^

Answer 18

oh good thats some relief :P

Answer 19

from additional practice sections. no way in ****** I would truth table that

Answer 20

shouldnt be hard to truth table it incase if u r forced to..

Answer 21

true

Answer 22

P Q R P V Q ~(P ^ Q) implies R

Answer 23

Consider the saying "All that glitters is not gold." What about "Not all that glitters is gold?" Which is the true statement? Are the two statements negations of each other? Write the negation of each statement.

Answer 24

K like that's All that glitters is gold for a negation
All that glitters is gold for the second... WOAH! similar sentences?

Answer 25

oh wait ... maybe it's ALl that glitters is not gold... oh wow. umm errr x) O_____________o

Answer 26

All that glitters is not gold

All that glitters is gold

Not all that glitters is gold

All that glitters is gold... whoa!!!!!!!! wha wha.a..a..a.a
unless that's all that glitters is not gold... wow umm err

Answer 27

original saying is this : if something glitters, it doesnt mean it is gold

Answer 28

true could be silver or copper

Answer 29

Consider the saying "All that glitters is not gold." What about "Not all that glitters is gold?" Which is the true statement? Are the two statements negations of each other? Write the negation of each statement.

Both statements are equivalent. negation wud be :-
All that glitters is gold

Answer 30

i could be wrong lol... my head is also spinning :o

Answer 31

yeah that's what I got too.. identical sentences I was like lolwut

Answer 32

by the way I got that assignment back with the cite previous result... apparently I wasn't the only one who got confused with the directions

Answer 33

lets try this :

P : All that glitters
Q : Gold

~P : All that NOT glitters
~Q : Not Gold

Answer 34

It was just state the proposition...oh wow like how can a lot of people know what the **** that cite previous result was ughhhhhh

Answer 35

I was like >:(

Answer 36

form two conditionals :

"All that glitters is not gold."
P -> ~Q

"Not All that glitters is gold."
~P -> Q

Answer 37

form truth table,
looks our initial thinking is incorrect. they dont seem to be equivalent now :o

Answer 38

dont forget
the negation of the universal quantifier
is equivalent to
the existential qualifier of the negation

Answer 39

argh this thing is confusing like "cite previous result"

Answer 40

he wrote and I quote "you didn't have to do that much. . . just state the proposition. " O M G I was like W T sdkfjsdafjslfdkfjdfsa;lfjsdklfjdslf;sdajfkdlsfjdlsfl;safjfklsdsdjfklsfjskljf

Answer 41

@UnkleRhaukus help

Answer 42

What is the question we on?

Answer 43

if i form conditional statements and create truth tables, they are not equivalent.

however they seem to be equivalent in common sense

Answer 44

this one :

Consider the saying "All that glitters is not gold." What about "Not all that glitters is gold?" Which is the true statement? Are the two statements negations of each other? Write the negation of each statement.

Answer 45

Those two statements say the same thing,

just because it glitters doesn't mean it is gold

both are true,
(they are not negations of one-another)

The negation is "All that glitters is gold"

(which happens to be false) [consider snow globes]
snow globes exist , snow globes glitter, snow globes are not gold ,

hence there exists something that glitters that is not gold

Answer 46

same thing just reworded differently?

Answer 47

makes sense :)
forming conditionals is a bad idea lol.. these are not conditionals in the first place.

"Exists" and "All" are the quantifiers to think around I see xD