If a number is nonzero, then the number is positive.
The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional.
For the statement "convergence implies boundedness," the converse statement would be "boundedness implies convergence."So, we are asking if "boundedness implies convergence" is a true statement.Pf//By way of contradiction, "boundedness implies convergence" is false.Let the sequence (Xn) be defined asXn = 1 if n is even andXn = 0 if n is odd.So, (Xn) = {X1,X2,X3,X4,X5,X6...} = {0,1,0,1,0,1,...}Note that this is a divergent sequence.Also note that for all n, -1 < Xn < 2Therefore, the sequence (Xn) is bounded above by 2 and below by -1.As we can see, we have a bounded function that is divergent. Therefore, by way of contradiction, we have proven the converse false.Q.E.D.
about seventy-four dollars
That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.
I believe the converse is: if 2x equals 6 then x equals 3 inverse: if x doesn't equal 3 then 2x doesn't equal 6 contrapositive: if 2x doesn't equal 6 then x doesn't equal 3
A biconditional is the conjunction of a conditional statement and its converse.
The conjunction of a conditional statement and its converse is known as a biconditional statement. It states that the original statement and its converse are both true.
It is the biconditional.
If lines lie in two planes, then the lines are coplanar.
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.
Yes
An integer n is odd if and only if n^2 is odd.
Converse
Switching the hypothesis and conclusion of a conditional statement.
The area of a square is 25 square meters if and only if the side length of the square is 5 meters
true
a biconditional"All triangles have 3 sides" and "A polygon with 3 sides is a triangle" can be combined as "A polygon is a triangle if and only if it has 3 sides."The phrase "if and only if" is often abbreviated as "iff".