trevor said:If I study, then I will not fail basket-weaving 101. If I do not play cards to often, then
I will study. I failed basket-weaving 101. Therefore, I played cards too often. Is this
statement valid (use truth tables to verify).
Joppy said:Have you constructed a truth table? Care to share? :). If not, I recommend breaking down all the words into a string of implications. For example, let A be the statement "I study", B be the statement "I failed basket-weaving" etc and use these to help with the truth table.
A truth table is a table used in logic to determine the truth or falsity of a statement based on different combinations of input values. It is a visual tool that helps in understanding the logical relationships between different propositions.
To validate a statement using a truth table, you must first list out all the possible combinations of truth values for the variables in the statement. Then, using logical operators such as "and," "or," and "not," you can determine the truth value of the entire statement for each combination of input values. If the statement is true for all combinations, it is considered valid.
A statement fails in a truth table when there is at least one combination of input values that results in a false statement. This means that the statement is not always true and is therefore considered invalid.
No, a valid statement will always result in a true statement for all possible combinations of input values in a truth table. If a statement fails in a truth table, it is not considered valid.
Truth tables provide a visual representation of the logical relationships between different propositions and can help in determining the validity or invalidity of a statement. They also allow for the identification of logical fallacies and contradictions within a statement, aiding in the understanding of logical arguments and reasoning.