Question

\[\forall A[(A \wedge A)\Leftrightarrow(A\vee A)]\]?

Answer 1

"For all (A and A) if and only if (A or A)."
Doesn't really make too much sense.

Answer 2

t/f

Answer 3

U mean for all A?

Answer 4

thats what i mean

Answer 5

Ah, I see, you do mean for all A, sorry...

Answer 6

True

Answer 7

(A and A) TFTF <-- isn't this same as A?
(A or A) <--- this is always true.

A and A <-----> A or A .... i guess this would be same as A

Answer 8

this is logically equivalent to "for all A|A" ???

Answer 9

Think he is taking a course in logic and set theory?

Answer 10

A=A, let me just prove that.....

Answer 11

true is right

Answer 12

this doesn't make any sense ... UnkleRhaukus you are playing around with logic ... right?

Answer 13

is my grammar off?

Answer 14

where do you use this notation or statement?
for all x| ...

Answer 15

um

Answer 16

mathematics?

Answer 17

Usually you would specify a set....

Answer 18

and how are you using it? UnkleRhaukus?

Answer 19

Is this related to your universal set question from before?

Answer 20

i mean for all sets

Answer 21

The expression For all x (x^2 is not 2) is ambiguous because no set has been specified.

So you would say For all x in R (for example) and then its false or if you specify N, then it's true.

Answer 22

A and A <===> A<====>A or A
???

Answer 23

I think the problem here (and the other question) is that it is not clear what "universe" we are talking about, math, logic, set theory (which one), etc...

Answer 24

it is true.

Answer 25

does it make sense?
for all x|x

Answer 26

when u have a proposition like this
\[ \large (\forall x)(P(x)) \]
then it is true whenever the predicate P(x) is true for all possible values of x.

Answer 27

\[ \large \forall x|P(x) \]
this makes sense but this sounds silly
for all x such that x

Answer 28

so in
\[ \large (\forall A)[(A\wedge A)\leftrightarrow(A\vee A)] \]
we can assume A is a proposition (there is no other option, actually).

Answer 29

in this example
\[ \large P(A):(A\wedge A)\leftrightarrow(A\vee A) \]
which is a tautology for every proposition A.

Answer 30

sorry i gotta go.

Answer 31

cya