A conditional statement is true if, and only if, its contrapositive is true.
This is not always true.
No. Consider the statement "If I'm alive, then I'm not dead." That statement is true. The converse is "If I'm not dead, then I'm alive.", which is also true.
A simple example of a conditional statement is: If a function is differentiable, then it is continuous. An example of a converse is: Original Statement: If a number is even, then it is divisible by 2. Converse Statement: If a number is divisible by 2, then it is even. Keep in mind though, that the converse of a statement is not always true! For example: Original Statement: A triangle is a polygon. Converse Statement: A polygon is a triangle. (Clearly this last statement is not true, for example a square is a polygon, but it is certainly not a triangle!)
Converses of a true if-then statement can be true sometimes. For example, you might have "If today is Friday, then tomorrow is Saturday," and "If tomorrow is Saturday, then today is Friday." Both the above conditional statement and its converse are true. However, sometimes a converse can be false, such as: "If an animal is a fish, then it can swim." and "If an animal can swim, it is a fish." The converse is not true, as some animals that can swim (such as otters) are not fish.
Conditional statements are also called "if-then" statements.One example: "If it snows, then they cancel school."The converse of that statement is "If they cancel school, then it snows."The inverse of that statement is "If it does not snow, then they do not cancel school.The contrapositive combines the two: "If they do not cancel school, then it does not snow."In mathematics:Statement: If p, then q.Converse: If q, then p.Inverse: If not p, then not q.Contrapositive: If not q, then not p.If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true.
If a conditional statement is true then its contra-positive is also true.
yes it is
Not necessarily. If the statement is "All rectangles are polygons", the converse is "All polygons are rectangles." This converse is not true.
A conditional statement may or may not be true.
An integer n is odd if and only if n^2 is odd.
it is true
It may or may not be true.
Well first you have to read the conditional statement and find out what the hypothesis is and what the conclusion is. Next you just switch the hypothesis and conclusion and put them in an if-then statement. Example: If someone is a football player, then they are an athlete. Hypothesis: someone is a football player Conclusion: they are an athlete Converse: If someone is an athlete, then they play football. *NOTE* You are allowed to change some of the words and just because the conditional statement is true doesn't mean that the converse will be true. *Hope this helps. Sorry its kinda longer then most answers.*
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.
not b not a its contrapositive
the converse of this conditional is true