The Logic Of Statement Equivalence: How To Prove Statements Are Equivalent.

when are two statements equivalent?

two statements are called logically equivalent if, and only if, they have identical truth values for each possible substitution of statements for their statement variables

Two statements are equivalent when they have the same meaning or truth value. In other words, if one statement is true, then the other statement is also true, and if one statement is false, then the other statement is also false.

For example, the statements 2+2=4 and 4=2+2 are equivalent, because they both have the same meaning and truth value. Similarly, the statements All dogs are mammals and No dogs are not mammals are equivalent, because they both express the same idea and have the same truth value.

To prove that two statements are equivalent, you need to show that they are logically equivalent by using logical laws and rules. This can be done by constructing truth tables, using logical equivalences, or applying the rules of inference.

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