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Correct. This is how in mathematical logic we express a statement like "all X are Y". You cannot express this directly, because you would have to say something like "Let ##C## be the set of all comedians. Then ##\forall x \in C, F(x)##. Unfortunately, in logic, a for-all symbol always runs over the entire universe - in this case, all people, so once you write ##\forall x## you imply ##\forall x \in X## and the qualification over ##C## is invalid.Miike012 said:The statements says all comedians are funny. The reason why I am asking the question is because to me the symbolic expression in the paint document which expresses that "All comedians are funny" implies that if you are a comedian then you must be funny.
So what I am saying, that "all comedians are funny" and "if you are a comedian then you are funny" are equivalent.
C(x) F(x) (1): C(x)->F(x) (2): ... (3): ...
T T ...
T F
F T
F F
Logic expression refers to a statement or equation that represents a logical relationship between two or more variables, usually using symbols such as AND, OR, and NOT. It is commonly used in computer programming and mathematics to represent logical operations.
Logic expressions are translated into English by breaking down the symbols and operations into words and phrases that convey the same logical meaning. For example, the symbol "&" might be translated as "and" and the symbol "!" might be translated as "not".
Translating logic expressions into English allows for easier understanding and communication of complex logical relationships. It also allows for easier troubleshooting and debugging in programming, as well as clearer explanations of mathematical concepts.
Some common keywords used in English when expressing logic include "and", "or", "not", "if", "then", "else", "implies", "equivalent", "for all", and "there exists". These keywords are used to represent logical operations such as conjunction, disjunction, negation, implication, and quantification.
Yes, there are some general rules and conventions for translating logic into English. For example, the order of operations is typically represented by parentheses in logic expressions, but in English, the words "not" and "and" are usually applied first, followed by "or". Additionally, the use of parentheses and proper punctuation is important for maintaining the correct logical meaning when translating into English.