Logical Equivalence Made Easy: Simplify (-p^q)v-(pvq) with Standard Rules

In summary, logical equivalence is a relationship between two statements or propositions where they have the same truth value in all possible scenarios. It is different from logical implication, which means that one statement being true guarantees the truth of the other statement. Some common symbols used to represent logical equivalence are the triple bar (≡), the double arrow (⇔), and the tilde (~). Examples of logically equivalent statements include "If it is raining, then the ground is wet" and "The ground is wet if it is raining." Logical equivalence is useful in solving problems as it allows us to simplify complex statements and make logical deductions.
  • #1
neil87
1
0
Use the standard logical equivalences to simlify the expression (-p^q)v-(pvq)...

fanx folks!
 
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  • #2
I did it.

Not foo hard.
 
  • #3


I would like to clarify that logical equivalence is a fundamental concept in logic and is not something that can be simplified or made easy. It is a complex concept that requires a thorough understanding of propositional logic and its rules.

That being said, to simplify the given expression, we can use the standard logical equivalences such as De Morgan's laws, distributive law, and identity law. Applying these rules, we can rewrite the expression as (-p∨q)∧(¬p∨¬q). This is equivalent to the original expression and can be verified using a truth table.

In conclusion, while there are rules and techniques that can help us simplify logical expressions, it is important to understand the underlying concepts and not oversimplify them. Logical equivalence is a crucial tool in logical reasoning and should be approached with a thorough understanding.
 

1. What is logical equivalence?

Logical equivalence is a relationship between two statements or propositions, where they have the same truth value in all possible scenarios. This means that if one statement is true, the other statement must also be true, and if one is false, the other must also be false.

2. How is logical equivalence different from logical implication?

Logical equivalence and logical implication are both relationships between two statements, but they are not the same. Logical equivalence means that the two statements have the same truth value, while logical implication means that one statement being true guarantees the truth of the other statement.

3. What are some common symbols used to represent logical equivalence?

Some common symbols used to represent logical equivalence are the triple bar (≡), the double arrow (⇔), and the tilde (~). These symbols are typically used in between two statements to show that they are logically equivalent.

4. What are some examples of logically equivalent statements?

Some examples of logically equivalent statements are "If it is raining, then the ground is wet" and "The ground is wet if it is raining." Another example is "All squares are rectangles" and "All rectangles are squares." In both cases, the two statements have the same truth value.

5. How can logical equivalence be useful in solving problems?

Logical equivalence is useful in solving problems because it allows us to simplify complex statements and make logical deductions. By using logical equivalence, we can break down a statement into smaller, equivalent statements that are easier to understand and work with. This can help us to find solutions and make logical arguments more effectively.

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