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any suggestion ( Book , Pdf , online resource , ... ) for solving problems about modal logic and intuitionistic logic and it would be really great if there was a solution for it .

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For modal logic I'm fond of Theodore Sider's Logic for Philosophy; I'm a mathematician who took a course on modal logic in the philosophy department using this book, and I found it a pleasant text. It's more rigorous than most philosophical logic texts, it's got plenty of exercises, and it has selected solutions in an appendix. It also has a short section on intuitionistic logic, but there are probably better sources for that.

There's a good amount of material that may not be of interest to mathematicians (counterfactuals, epistemic logic, tense logic), so for your purposes it may be better to check out from a library than actually purchase a copy (unless you're also interested in the philosophical aspects).

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