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No, not always. It depends on if the original biconditional statement is true. For example take the following biconditional statement:
x = 3 if and only if x2 = 9.
From this biconditional statement we can extract two conditional statements (hence why it is called a bicondional statement):
The Conditional Statement: If x = 3 then x2 = 9.
This statement is true. However, the second statement we can extract is called the converse.
The Converse: If x2=9 then x = 3.
This statement is false, because x could also equal -3. Since this is false, it makes the entire original biconditional statement false.
All it takes to prove that a statement is false is one counterexample.
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Is the converse of a biconditional statement always true?
Yes
is this statement true or falseA biconditional statement combines a conditional statement with its contrapositive.?
false
A statement that describes a mathematical object and can be written as a true biconditional statement?
Definition
The converse and inverse of a conditional statement are logically equivalent?
This is not always true.
If a statement is true is it converse also true?
Not necessarily. If the statement is "All rectangles are polygons", the converse is "All polygons are rectangles." This converse is not true.
