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Tek1Atom
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Homework Statement
By providing a truth table, show that the following logic statement is a tautology:
p ∧ (p → q) → qAny help will be much appreciated.
Thank You
Tek1Atom said:Thank you DH, that was very helpful. My final question is, does it matter which way we write down the truth table?
e.g.
which one is correct?
p | q | P → q | p∧(p→q)→q
---------------------------
T | T | T | T
T | F | F | T
F | T | T | T
F | F | T | T
OR
p | q | P → q | p∧(p→q)→q
---------------------------
F | F | T | T
F | T | T | T
T | F | F | T
T | T | T | T
A Tautology is a logical statement that is always true, regardless of the truth values of its individual components or variables.
To prove a statement is a Tautology using a Truth Table, you must construct a table that lists all possible combinations of truth values for the variables in the statement and then evaluate the statement for each combination. If the statement is true for every possible combination, it is a Tautology.
No, a statement cannot be both a Tautology and a Contradiction. A Tautology is always true, while a Contradiction is always false. A statement must be one or the other, not both.
Some examples of Tautologies include "A or not A", "If it is raining, then it is wet", and "All squares have four sides". These statements are always true regardless of the truth values of their components.
Proving a statement is a Tautology is important because it allows us to establish the validity and certainty of the statement. It also helps us to identify and eliminate potential errors or inconsistencies in our reasoning or arguments.