Suggestions for studying logic

Question

I am a High-School Student and I wanted to study logic.Now , as a background , I have read Set theory, some Geometry and Induction and I thought it would be sufficient enough to begin self studing an elementary subject like Logic.

I started from reading some lecture notes , but they were kind of confusing. The Definitions are easy to read but sometimes they explain concepts in a hand wavy way and expects me to automatically understand the concept without any second thoughts (In a way , they are not formal and concise enough for me).I guess I have been reading the wrong logic lecture notes.

Sometimes , they have simple definitions but end with hard exercises witch you need a lot of experience to solve. But How Am I expected to solve those problems if I am just studying logic from ground zero. For example ,you are told to do exercise 1.0 for which you need knowledge of chapter 2.0.This makes me frustrated.

At this point , I have 3 options,

$1$.Download multiple pdf from multiple sources :This is time consuming , but I am definitely willing to do the hard work to read from all of them and gain some insight about this subject. The problem is from reading multiple books(good or bad) ,The things I learn from from them might conflict with each other in my head and I might end up learning nothing good.

$2$.Reading One good textbook and going downwards:This might be a good option , but the problem is that ,again , I have 0 experience about this topic. If this is a good option , then It will definitely help me to give some advise about witch textbooks I should start with if I want to learn logic in a Concise , Rigorous and formal way.

$3$.Just Give up : Assuming I am a high school student , I might be asking for too much and it might ruin my future student carrier somewhat. So I can just give up and learn this stuff when I grow up .Maybe I should give up because I am not hard working and smart enough to study mathematics like this.

It is true That I have 0 experience about this topic and only started to read things like proposition-logic and truth tables.Thats why I am asking this question.Which option I should choose?

Edit:Here is a short summary of my background.I am at hi-school studying things like set theory,function,algebra .But still , often I like to go out of my safezone and study things like abstract algebra,linear algebra,calculus,tensor calculus etc.But first I wanted to establish a firm grasp on the foundations of mathmatics (things like proposition logic and axiomatic set theory).I want to also study it rigorously and formally, so that it becomes my second nature.According to my second option , I should definitely choose a good book(like mendelson) and not start with something totally unworthy because that will be a waste of my time.Why do like to study it rigorously and formally?Because that way I can resolve apparent paradoxes and build up my mathematical foundation without any "structural issues".I also like to research about something if I find any doubt,but I definitely don't like the moments when I find out that what I have learned so far was just a lie and start over again. (that happened to me many time because of bad textbooks and teaching methods)

Peter Smith, Formal Logic, R.Jeffrey, Formal Logic, S.C.Kleene, Mathematical Logic, R.Smullyan, First-order Logic. — Mauro ALLEGRANZA, Oct 13 '20 at 12:48
To get you started, may I humbly suggest the tutorial that comes with my DC Proof freeware downloadable at my homepage http://www.dcproof.com Hints and full solutions are provided for each exercise. — Dan Christensen, Oct 13 '20 at 15:14
My recommendations, based on what you've said, are Propositional and Predicate Calculus: A Model of Argument by Derek C. Goldrei (2005) and First Course in Mathematical Logic by Patrick Suppes and Shirley Hill (1964; reprinted by Dover in 2002; and DON'T get the Kindle edition). — Dave L. Renfro, Oct 13 '20 at 16:18
Is "Introduction To Mathematical Logic By Mendelson" a good book to study logic rigorously? — Kripke Platek, Oct 13 '20 at 16:31
Mendelson's book is probably too advanced from what you've said. If the two books I mentioned are too pedestrian for you, then maybe look at Logic for Mathematicians by A. G. Hamilton. Enderton's book is probably better (certainly not as comprehensive, which is a drawback for you at this point) if you're at the level for Mendelson. — Dave L. Renfro, Oct 13 '20 at 16:37
I am right now reading it , and it seems way better than what I have read a couple of weeks ago . And "Mendelson's book is probably too advanced from what you've said" What does "advanced" exactly mean here? (By the way , Mendelson's book about logic seems to be way better for me than many other books that I have read a couple of weeks ago,probably perfect for me?) — Kripke Platek, Oct 13 '20 at 16:46
If Mendelson doesn't seem excessively advanced for you, then Suppes/Hill's book is definitely too low level for you, and Goldrei's book might be too long-winded for you (but in my opinion, it's excellent for self-study and it has many explanatory tangents that other books omit, as the author expects such things to be taken care of by the teacher). Hamilton still might be worth having (if you have the money and space), but if you can continue through Mendelson, then I recommend just staying with Mendelson. — Dave L. Renfro, Oct 13 '20 at 16:58
Some of the suggestions I gave in my answer to Where to begin with foundations of mathematics might be of use, and then there's Peter Smith's very extensive Teach Yourself Logic: A Study Guide. — Dave L. Renfro, Oct 13 '20 at 17:02
What does "advanced" exactly mean here? --- I forgot about this. By "advanced", I meant mathematical maturity, and not technical expertise in later-studied subjects like Galois theory, measure theory, complex analysis, topology, etc. — Dave L. Renfro, Oct 13 '20 at 17:11
I guess Option two will be sufficient for me.(Thanks for your suggestion about some good books I can read ,but as you said , I will be just staying with Mendelson).Not exactly sure about my mathmatical maturity (As a reference , I have been watching eigencrhises series on tensors and tensor calculus just to get a glimpz about his subject).I guess the third Option can be discarded for a latter day :) — Kripke Platek, Oct 13 '20 at 17:32
By the way, Dan's website has bogus articles and his proof system is useless for actual mathematical work. I know this is an old post but this comment is to inform readers who may otherwise get duped. =) — user21820, Jun 27 '21 at 12:21

Suggestions for studying logic

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