Can truth exist without falsehood?

I dont think so if false is the opposite of truth and natural law always has its opposite 

Jehovah is described as “the God of truth,” and he said of himself: “I do not change.” (Psalm 31:5; Malachi 3:6) About God, Jesus said: “Your word is truth.” (John 17:17) That truth is revealed in the divinely inspired Scriptures, the Bible. It instructs us and equips us “for every good work.”—2 Timothy 3:16, 17.

Sometimes, especially if God is not watching.

Can "truth" exist without falsehood?

It can and the term describing that is called "faith".

And by the way in any philosophy study bar one we should

not mix up "truth" with the description "falsehood" (as the

latter is an obviously staged term and not recommended 

to be used with truth as something discovered and invented

- out of nothing if you like (or not).

The much better philosophy question, and designation is that

of truth or FALSITY.

As in objective or subjective we may say (believers in the latter

who cannot agree on there being a true philosophy environment

are mistaken).

As it is undoubtedly true that Philosophy exists as a particular

entity the question may arise about that entity's presence, and

it's independent study, what can be worthwhile so to speak. 

For example it is a subjective and behavioural falsehood to

say that the entity that is Philosophy has anything to do with

"definition-ism", and false, common "deceitfulness".

Preconceived ideas like defining something and calling something

deceitful is an ordinary (real) part of behaviour which has more

to do with "faith" than Philosophy. Hence the mistaken connection

of those behaviours with something like "falsehood" ...for ANY

term and the behaviour associated with the true writing of such

can easily be shown to be independent of something like true

Philosophy entity, a knowledge gathering area.

For anyone can have a subjective understanding and a learned

subjective knowledge that is totally different from someone

else's learned knowledge. Both frequently miss a connection

with Philosophy-area-study because of some mistake in

their learned behaviour for example.. learning from a mistake

previously made by another subjective falsehood. 

And I think that I have shown previously that "subjective falsehood"

based on faith such as religious faith have more in common the

further one goes back in historical evidence so to speak (it can 

be said both in faithful and secular, non-faith based historical

evidence..) . That is that it is entirely possible that the mistake

of learning something wrong (learning that a true Philosophy

knowledge area doesn't exist) was tacitly agreed between

subjectives and religions, that a Philosophy knowledge area

DOES NOT Exist. 

Fortunately the truth is now that Philosophy and it's truthful,

environmentally and critically secure knowledge DOES exist

whether "Subjective philosophers" and the faithfully religious

philosophy's can agree or not.

Falsehood can exist without truth and truth can exist without falsehood. More commonly they both exist but incomplete truth can amount to falsehood when the intent is to deceive. 

The concept of truth can't exist without the concept of falsehood; they define each other, but truth may be spoken without speaking falsehood. And vice versa. 

Use some common sense and you aren't clever.

Of course.  

Imagine always telling the truth.  Then imagine always lying.

Always lying would make no sense at all.

You cant have falsehood without truth.  

But truth is self-sufficient without falsehood.

Can Light exist without darkness?

"Light is a Living Spirit;"

"Beams from Meher Baba;"

"The Path of the Higher Self;"

https://www.mothermeera.com/ 

Of course it can, even though sometimes I think there is an infinite well of stupidity that people draw from.