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Let's take an example.
If it is raining (then) the match will be cancelled.
A conditional statement is false if and only if the antecedent (it is raining) is true and the consequent (the match will be cancelled) is false. Thus the sample statement will be false if and only if it is raining but the match still goes ahead.
By convention, if the antecedent is false (if it isn't raining) then the statement as a whole is considered true regardless of whether the match takes place or not.
To recap: if told that the sample statement is false, we can deduce two things: It is raining is a true statement, and the match will be cancelled is a false statement. Also, we know a conditional statement with a false antecedent is always true.
The converse of the statement is:
If the match is cancelled (then) it is raining.
Since we know (from the fact that the original statement is false) that the match is cancelled is false, the converse statement has a false antecedent and, by convention, such statements are always true.
Thus the converse of a false conditional statement is always true. (A single example serves to show it's true in all cases since the logic is identical no matter what specific statements you apply it to.)
If you are familiar with truth tables, the explanation is much easier. Here is the truth table for A = X->Y (i.e. A is the statement if X then Y) and B = Y->X (i.e. B is the converse statement if Y then X).
X Y A B
F F T T
F F T T
T F F T
F T T F
Looking at the last two rows of the A and B columns, when either of the statements is false, its converse is true.
What else can I help you with?
What is a true statement that combines a true conditional statement and its true converse?
always true
Is the converse of a true if-then statement never true?
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.
Can polynomials with the same graph have different roots?
False! If the graph is exactly the same, then the x-intercepts will be the same which implies the roots are them same. However, you can have the same roots and different graphs. So while the first statement is true, the converse if not.
What is the converse of the statement below X - y?
y -> x
What is 5 5 5 5 5 equals 26?
It is a FALSE statement.It is a FALSE statement.It is a FALSE statement.It is a FALSE statement.
Is the converse of a true conditional statement always false?
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.
Is this statement true or false The conditional is the negation of the converse?
The statement is false. The conditional statement "If P, then Q" and its converse "If Q, then P" are distinct statements, but the negation of the converse would be "It is not the case that if Q, then P." Thus, the conditional and the negation of the converse are not equivalent or directly related.
is this statement true or falseThe inverse is the negation of the converse.?
false
What is a Converse statement?
A converse statement is a statement is switched to make the statement true or false. For example, "If it is raining, then we will not go to the beach" would be changed to, "If we go to the beach, then it is not raining."
Is the converse of a true if-then statement always true?
No.
What is proof by Converse?
Proof by Converse is a logical fallacy where one asserts that if the converse of a statement is true, then the original statement must also be true. However, this is not always the case as the converse of a statement may not always hold true even if the original statement is true. It is important to avoid this error in logical reasoning.
Is The converse of a biconditional statement is always true?
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.
Is the converse of a biconditional statement always true?
Yes
Is the conditional is the negation of the Converse?
No, the conditional statement and its converse are not negations of each other. A conditional statement has the form "If P, then Q," while its converse is "If Q, then P." The negation of a conditional statement would be "P is true and Q is false," which is distinct from the converse. Thus, they represent different logical relationships.
What is a true statement that combines a true conditional statement and is its true converse?
always true
What is a true statement that combines a true conditional statement and its true converse?
always true
What is the converse of the contrapositive of a statement?
Look at the statement If 9 is an odd number, then 9 is divisible by 2. The first part is true and second part is false so logically the statement is false. The contrapositive is: If 9 is not divisible by 2, then 9 is not an odd number. The first part is true, the second part is false so the statement is true. Now the converse of the contrapositive If 9 is not an odd number, then 9 is not divisible by two. The first part is false and the second part is true so it is false. The original statement is if p then q,the contrapositive is if not q then not p and the converse of that is if not p then not q
