Wiki User
∙ 6y agoWant this question answered?
Be notified when an answer is posted
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.
If lines lie in two planes, then the lines are coplanar.
Yes
Switching the hypothesis and conclusion of a conditional statement.
No, it is not a definition: it is an imperative statement requiring you to do something!
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.
A biconditional is the conjunction of a conditional statement and its converse.
It is the biconditional.
If a number is nonzero, then the number is positive.
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.
If lines lie in two planes, then the lines are coplanar.
Yes
An integer n is odd if and only if n^2 is odd.
The converse of this conditional statement would be: if I am in the south, then I am in Mississippi. It essentially swaps the hypothesis and conclusion of the original conditional statement.
The inverse of a conditional statement switches the hypothesis and conclusion. The converse of a conditional statement switches the hypothesis and conclusion. The contrapositive of a conditional statement switches and negates the hypothesis and conclusion.
Converse
Switching the hypothesis and conclusion of a conditional statement.