How do you know if logically equivalent?
Two logical statements are logically equivalent if they always produce the same truth value. Consequently, p≡q is same as saying p⇔q is a tautology.
Why any two tautologies are logically equivalent?
If all tautologies are sentences, then no tautologies are logically equivalent. So, because tautologies always have the same truth value (namely, true), they are always logically equivalent. Moreover, two contradictions (sentences (or propositions) whose truth value is always “false”) are also logically equivalent.
What is an equivalent statement example?
Take for example the statement “If is even, then is an integer.” An equivalent statement is “If is not an integer, then is not even.” The original statement had the form “If A, then B” and the second one had the form “If not B, then not A.” (Here A is the statement ” is even”, so “not A” is the statement ” is not even” …
Are all logically true sentences logically equivalent?
A pair of sentences are logically equivalent just if it is not possible for them to differ in truth value. A sentence is logically true just if it is not possible for it to be false. Hence any two logically true sentences will necessarily both be true, and so it is not possible for them to differ in truth value.
What does logically inconsistent mean?
Logical inconsistency is about using arguments which are not internally consistent. Personal inconsistency is about accusing others of inconsistency.
What is the definition of logical equivalence?
To have a better understanding of why the two statements are true, one must know the definition of logical equivalence. Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and the second statement can also be true in its own context,…
How do you determine if two statements are logically equivalent?
The following table depicts how two statements that are logically equivalent correlate with one another, whether both are true, one is true and one is false, or if both are false. As long as both statements have the same meaning or coverage, then this table holds true and the statements will always be connected and be logically equivalent.
What is an equivalent statement of the form?
Therefore, an equivalent statement would be of the form. Hence, we would say, Henry, is a teacher or Paulos is not an accountant. Furthermore, there are times when we would instead state reasons for why two statements are logically equivalent, rather than constructing a truth table.
What is the difference between logically equivalent and contradictory?
While the statements may be contradictory, they are logically equivalent because they are covering the same topic. The statements can be derived from one another to determine which is true, which are false, or if both are true or false, based on the topic.