Hello .~!@# !.~!@# said:Homework Statement
1) (∀xεℝ)((x≠0)→((∃yεℝ)(xy=1)
2) (∃yεℝ)(∀xεℝ)((x≠0)→(xy=1))
Homework Equations
∃ - there exists
∀ - for all
→ implication
The Attempt at a Solution
The brackets and implication are throwing me for a loop
1) for all real numbers, there exist another real number such that their product is 1. TRUE
2) There exists a real number y, such that any real number and y will have a product of 1. False.
?
Predicate logic is a formal system of logic that is used in mathematics, philosophy, linguistics, and computer science. It is used to represent and reason about propositions that contain variables, quantifiers, and logical connectives.
To solve a predicate logic equation, you must first translate the given statements into symbolic notation using quantifiers, variables, and logical connectives. Then, you can use rules of inference and logical equivalences to manipulate the statements and reach a conclusion.
The most common symbols used in predicate logic include the universal quantifier (∀), the existential quantifier (∃), logical connectives (¬, ∧, ∨, →, ↔), and parentheses for grouping. Variables are also commonly used to represent objects or elements in the statements.
To check the correctness of your solution, you can use truth tables to evaluate the truth values of each statement in your solution. If the truth values of all statements match, then your solution is correct.
Some tips for solving complex predicate logic equations include breaking down the statements into smaller parts, using logical equivalences to simplify the statements, and using rules of inference to make deductions. It is also helpful to practice regularly and familiarize yourself with the common symbols and rules of predicate logic.