I was taking a look at Gensler's Introduction to Logic but the reviews suggest that it might be better as a second text than a first. What books can HN recommend instead?
If you're looking for something good that covers the basics in more detail, I recommend Epp's Discrete Mathematics with Applications. This covers material like truth tables, valid and invalid arguments, quantifiers, etc.
In addition to the treatment of logic, it also has chapters on induction, combinatorics, graphs and trees, analysis of algorithms, finite state automata, etc.
I chose this book when I taught a college course in "math for computer science majors", and it was a great choice overall. It's probably the most beginner-friendly of any book covering this material, and it's extremely organized and well written. Costs an arm and a leg to buy new, so buy a used copy of an older edition.
https://web.mat.bham.ac.uk/R.W.Kaye/logic (not very helpful, lots of broken links, just look at the book instead)
I also like Logic in Computer Science by Huth and Ryan, cited in another comment here. It is much more comprehensive and has a lot more about logic applications in computer science.
You can buy a second hand copy of an older edition for a few dollars.
Maybe you have to read it twice.
So what?