Question 1133807: Which of the following statements is false?
A. Mathematical definitions should be written as biconditional statements.
B. In a conditional statement, the "if" clause is called the hypothesis.
C. In a conditional statement, the hypothesis and the conclusion can be interchanged without affecting the validity of the statement.
D. A statement formed by connecting two statements with the word "and" is called a conjunction
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A is true because it's true all the time.
B is true because it's true all the time.
C is not true because it's true only some of the time.
D is true because it's true all the time.
your answer is C as far as i can tell.
the hypothesis and the conclusion cannot be inter-changed and the statement always be true.
they may be true some of the time but may not be true some of the time.
if the original statement is true and the converse statement is true, then you have a bi-conditional statement.
an example would be:
if an object is a triangle then the sum of the interior angles of the object is equal to 180 degrees.
the converse statement would be if the sum of the interior angles of an object is equal to 180 degrees, then the object is a triangle.
if the original statement is true and the converse statement is true makes the original statement a biconditional statement and, in this case, a mathematical definition as well.
however, just because the original statement is true does not always make the converse true.
consider:
if a girl is 6 feet tall then she is a tall girl.
the converse would be if a girl is tall, then she is 6 feet tall.
while the original statement is true, the converse statement is not always true.
the girl can be 7 feet tall, or 8 feet tall.
she does not have to be 6 feet tall.
statement C says that the hypothesis and the conclusion can be inter-changed without affecting the validity of the statement.
this is not true all of the time, therefore it must be false.
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