conditional and contrapositive
+
converse and inverse
conditional and contrapositive + converse and inverse
conditional and contrapositive + converse and inverse
conditional and contrapositive + converse and inverse
The statement "if not p, then not q" always has the same truth value as the conditional "if p, then q." They are logically equivalent.
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.
true
Not always. For example, X is equal to or less than 6 is not the same as X is equivalent to 6.
Statements A and B contain variables, as they do not specify a numerical value, and could be different in different circumstances. However, 80 mph and 27 points are constants that always have the same value.
They are the same. the absolute value is always positive
If I said "I always lie" and it's true, then I have spoken the truth and I don't always lie.By the same token if I say "I always lie" and it's a lie, then I say the truth sometimes.The man lies when he says he always lies.
Nothing. The truth is, they have always been different.
Yes, it is.