Statements that are always logically equivalent are those that yield the same truth value in every possible scenario. Common examples include a statement and its contrapositive (e.g., "If P, then Q" is equivalent to "If not Q, then not P") and a statement and its double negation (e.g., "P" is equivalent to "not not P"). Additionally, the negation of a statement is logically equivalent to the statement's denial (e.g., "not P" is equivalent to "if not P, then false"). These equivalences play a crucial role in logical reasoning and proofs.
This is not always true.
Logically invalid statements.
An obverse statement is logically equivalent.
Two Venn diagrams are considered logically equivalent if they represent the same set relationships and overlap among the groups depicted. This means that the areas shaded in each diagram correspond to the same logical statements or conclusions about the sets involved. If the diagrams show different relationships or shading, they are not logically equivalent. Thus, the equivalence depends on the accuracy of their representation of the relationships between the sets.
Not always. For example, X is equal to or less than 6 is not the same as X is equivalent to 6.
No.
Contrapositive
a conditional and its contrapositive
This is not always true.
Logically invalid statements.
A Contrapositive statement is logically equivalent.
An obverse statement is logically equivalent.
syllogism
Two Venn diagrams are considered logically equivalent if they represent the same set relationships and overlap among the groups depicted. This means that the areas shaded in each diagram correspond to the same logical statements or conclusions about the sets involved. If the diagrams show different relationships or shading, they are not logically equivalent. Thus, the equivalence depends on the accuracy of their representation of the relationships between the sets.
The statement "If not q, then not p" is logically equivalent to "If p, then q."
A conclusion logically follows from other statements when it is a necessary inference based on the information provided. In logical reasoning, a conclusion is reached by applying valid reasoning rules to the given premises. If the conclusion can be drawn directly from the premises using these rules, it is said to follow logically.
Not always. For example, X is equal to or less than 6 is not the same as X is equivalent to 6.