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Today's tutorial covers how to negate logical statements, where true statements can be changed to false and vice versa. Symbolically, statements are represented using lowercase letters, with negation denoted by a tilde. For example, "Carlos likes donuts" (p) becomes "Carlos does not like donuts" (¬p). Another example is "It's not going to rain tomorrow" (q), which becomes "It is going to rain tomorrow" (¬q). The tilde symbol is used to indicate negation in these logical statements.