Logic basics

Question

If i have a statement like :

"No large birds live on honey" where domain is set of all Birds 

Here let Q(x) : x is a large bird 

R(x) : lives on honey  

CAn i write this is

∀x (∽Q(x)-->R(x)) ..is it right ?

and what about this ∀x (Q(x)-->∽R(x)) 

Comments

yes 1st one is correct

2nd one large birds not lives on honey

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@srestha
So second also mean same ryt ?

And bdw in Rosen it is given that

∽∃(Q(x)⋁R(x)) i am not getting this :(

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srestha How 1st is right?

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what is meaning of 1st stmt?

Q(x) : x is a large bird
~Q(x) : x is a bird other than large bird

and it is also given domain is set of all Birds
So, 1) is the stmt telling  " all other bird other than large birds live on honey"

is it not same as
"No large birds live on honey"

See the stmt here https://gateoverflow.in/45363/logic-basic

Answer 1

Note: The cutting in statement 2 solution is just a correction. Not any symbol or something.

Comments

yes i got my mistake :) I am right now doing that thing only breaking parts and then analyse it

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:)

Answer 2

∀x (∽Q(x)-->R(x)) =>all  birds  which are not large(i.e small )birds live on honey .but it is not mentioned in the statement.so its not correct

∀x (Q(x)-->∽R(x)) => all  large birds do not live on honey.its correct.

Comments

oh yes i agree thanks :)