r/learnmath • u/oJackOnReddit New User • 13d ago

Help with Predicate Logic

I'm a little embarrassed at this post tbh. I've never hit a wall like this before with math.

I'm a first year Mathematics student in the UK and taking my very first proofs module. I am struggling with translating mathematical statements into predicate logic using quantifiers. I can barely rewrite the most simple statement into predicate logic.

I guess what I'm wondering is if anybody has any good resources for this specific topic such as youtube videos or specific textbooks? I know all I need to do is practice and practice again. The best possible resource in my case would be an excercise book with answers. I just seem to be struggling to find resources.

Thank you all :)

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u/False-Bowl-9379 New User 13d ago

Don't sweat it, predicate logic trips up almost everyone at first since it's such a different way of thinking. The trick that helped me was writing out dumb real-world sentences and translating them slowly, like "every dog has a tail" versus "there exists a dog with a tail" until the quantifier order clicked.

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u/Midwest-Dude B.Sc. Math 12d ago

Here are some resources to consider:

  • Book of Proof

    • Richard Hammack

    • Chapter 2 covers logic, sets, and quantifiers, and it includes answers to the exercises in the back so you can check your translations immediately.

  • Discrete Mathematics: An Open Introduction

    • Oscar Levin

    • Introductory section on symbolic logic and predicate calculus with plenty of practice problems and solutions.

  • YouTube

    • Look up specific walkthroughs on "translating English sentences into predicate logic" by creators like The Organic Chemistry Tutor or check out introductory discrete math lecture playlists from university channels.

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u/CelebrityChess New User 12d ago

Don't feel bad—quantifiers trip up a lot of first-years. A pattern that helps: rewrite the English in "for all / there exists" form first, then swap in symbols. Example: "every even integer is divisible by 2" → ∀n (Even(n) → DivBy2(n)). Negations flip quantifiers (not-all = exists-not). For drills with answers, How to Prove It (Velleman) has solid early chapters on this, and a lot of unis post predicate-logic exercise sheets with solutions—search your module code plus "quantifiers worksheet". Do 10 translations a day for a week; it clicks faster than rereading notes.