What is the Difference Between Algebra and Propositional Calculus/Logic?

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Hello fellow fans of love! I am attempting to create an understanding of algebra, so I am prepared when I continue my education.

Background: When I was last in school, I failed the entrance exam (twice) for algebra. I took the alternative Logic instead. My dean urged me to take the prerequisite because Logic was generally considered harder than College Algebra. I was surprised when the questions in Logic came naturally to me and I got 100% with ease. Over 10 years later I was diagnosed (late) with ADHD.

Are algebra and propositional calculus both considered symbolic logic and what are the differences between how these two are logically processed?

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Algebra is not usually considered symbolic logic. Logic is a different area of mathematics to algebra (though also an area of philosophy and computer science).