Equivalence
Two statements are logically equivalent if and only if they have identical truth table values
Equivalence, in mathematics and logic, refers to two expressions or statements that have the same meaning or truth value. More specifically, two mathematical expressions are said to be equivalent if they produce the same output when they are evaluated, whereas two logical statements are equivalent if they always have the same truth value.
For example, the expressions 2 + 3 and 5 are equivalent since both produce the same result when evaluated. Similarly, the logical statements All birds can fly and No birds cannot fly are equivalent since they both express the same idea.
There are many different methods for proving equivalence between mathematical expressions or logical statements, depending on the specific context. Some common techniques include simplifying expressions using algebraic rules, applying logical laws and rules of inference, or using truth tables to compare different combinations of inputs and outputs.
Overall, equivalence is an important concept in mathematics and logic since it allows us to manipulate and rewrite expressions or statements in different ways without changing their underlying meaning or truth value.
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