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Homework Statement
Determine if the following is a tautology:
((p → q) Ʌ (q → p) → (p Ʌ q)
I don´t know how to show this. Can somebody pls show me all the steps
Cyosis said:Make the following table:
p|q|p → q|q → p|(p → q) Ʌ (q → p)|p Ʌ q|((p → q) Ʌ (q → p) → (p Ʌ q)
T|T|
T|F|
F|T|
F|F|
Now finish this table, if the last column yields true for all possible values for p and q then ((p → q) Ʌ (q → p) → (p Ʌ q) is a tautology.
A tautology is a statement or formula that is always true, regardless of the truth values of its components. It is important to show if something is a tautology because it helps us to identify logical fallacies and ensure the validity of our arguments.
To show if something is a tautology, we can use truth tables or logical equivalences to demonstrate that the statement is always true, regardless of the truth values of its components.
Some examples of tautologies include "Either it will rain tomorrow or it will not rain tomorrow" and "All cats are either black or not black". These statements are always true, regardless of the truth values of their components.
A tautology is a statement that is always true, while a contradiction is a statement that is always false. In other words, a tautology is a statement that is logically redundant, while a contradiction is a statement that is logically impossible.
In scientific research, we strive for accuracy and precision in our findings. Tautologies offer no new information and can be seen as a weakness in the argument. Therefore, it is important to avoid tautologies in scientific research to ensure the validity and reliability of our findings.