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aorick21
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Prove x <=> y is logically equivalent to (x-->y) ^ ((~x)-->(~y)).
aorick21 said:Prove x <=> y is logically equivalent to (x-->y) ^ ((~x)-->(~y)).
TimNguyen said:I'd just use a truth table.
If you don't know what that is, then I don't think you belong in math.
Logical equivalence refers to the relationship between two statements or propositions that have the same truth value. This means that if one statement is true, the other statement will also be true, and if one statement is false, the other statement will also be false.
The statement x <=> y means that x and y are logically equivalent. This means that x and y have the same truth value and can be substituted for each other in any logical expression without changing its truth value.
This expression is a logical statement that is equivalent to x <=> y. It is read as "if x implies y, and if not x implies not y." This means that if x is true, then y must also be true, and if x is false, then y must also be false.
The logical equivalence of x <=> y and (x-->y) ^ ((~x)-->(~y)) can be proven by constructing a truth table for both statements. The truth table will show that the two statements have the same truth values for all possible combinations of truth values for x and y.
Understanding logical equivalence is important in fields such as mathematics, computer science, and philosophy. It allows us to simplify complex logical expressions and to prove the validity of arguments and statements. It also helps in identifying logical fallacies and inconsistencies in reasoning.