Tanslate each of these statements into logical expressions using predicates, quan- tifiers, and logical connectives. A) Not all cats can jump high. Assume the domain is all animals. B) Some cats hate all dogs. Assume the domain is all animals. C) No drivers obey the speed limit if they are in a hurry. Assume the domain is all people.
Tanslate each of these statements into logical expressions using predicates, quan-
tifiers, and logical connectives.
A) Not all cats can jump high. Assume the domain is all animals.
B) Some cats hate all dogs. Assume the domain is all animals.
C) No drivers obey the speed limit if they are in a hurry. Assume the domain is all
people.
1) In logical expressions, predicates, quantifiers, and logical connectives are used to represent statements and relationships between statements.
2) A predicate is a statement that defines a property or a relationship between objects.
- Example, in expression "Cat(x)", "Cat" is a predicate that represents the property of being a cat, and "x" is a variable that represents an object.
3) Quantifiers are symbols that specify the scope of the variables in a logical expression.
- Example, the quantifier "∀x" means "for all x in the domain", while the quantifier "∃x" means "there exists x in the domain".
4) Logical connectives are symbols that combine two or more statements into a new statement.
- Example, the logical connective "∧" represents the logical "and" operator, while the logical connective "→" represents the logical "implies" operator. The logical connective "¬" represents negation.
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