Logic Symbols Explained

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its super common to open a math, computer science, or physics textbook and have mathematical symbols thrown at you that you never even learned how to read. here's a list of logical symbols that can help you improve your math comprehension!

symbol: A ⇒ B meaning: “If A, then B.” In other words, “A implies B.” In other words, “If A is true, then B is true.” example: x = 2 ⇒ x + 3 = 5

symbol: A ⇔ B meaning: “A if and only if B.” In other words, “If A is true, then B is true. If A is false then B is false.” example: x = 2 ⇔ x + 3 = 5

symbol: ∵ meaning: “Because” example: x + 3 = 5 ∵ x = 2

symbol: ∴ meaning: “Therefore” example: x = 2 ∴ x + 3 = 5

symbol: ∀ meaning: “For all”/“For every” example: ∀ x such that x is an integer, x + 2 is an integer

symbol: ∃ meaning: “There is at least one” example: ∀ x where x is an integer, ∃ y where y is an integer so that y > x

symbol: ∃! meaning: “There is only one” example: ∀ x where x is an integer, ∃! y where y is an integer and x-y = 1

symbol: ∈ meaning: “Is in” or “in,” depending on context. example: ∀ x ∈ R, ∃ y ∈ R so that y > x (R is the set of real numbers)

symbol: A := B meaning: “Let A equal B.” or “A, which has been defined to be equal to B,” depending on context. example: A := R (The set A is defined to equal the set of real numbers)

symbol: s.t. or | meaning: “Such that”/“So that” example: ∀ x ∈ R, ∃ y ∈ R s.t. y > x

there are tons of other types symbols i can go over in the future like set and function notation if you guys are interested, but these logical symbols are crucial for reading proofs.