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Ask us anythingIf the statement If I am hungry then I am not happy is assumed to be true is its converse If I am not happy then I must be hungry also always true?
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Is the converse of a biconditional statement always true?
Yes
The converse and inverse of a conditional statement are logically equivalent?
This is not always true.
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.
If the statement If I am hungry then I am not happy is assumed to be true is its inverse If I am not hungry then I must be happy also always true A. No B. Yes?
No
If the statement If I am hungry then I am not happy is assumed to be true is its inverse If I am not hungry then I must be happy also always true A.No B.Yes?
It’s no
If the statement If I am hungry then I am not happy is assumed to be true is its converse If I am not happy then I must be hungry also always true?
The Answer: NO
If the statement If it is cold then you wear a jacket is assumed to be true is its converse If you wear a jacket then it must be cold also always true?
No, it must not be true.
Is the converse of a true if-then statement always true?
No.
Is the converse of a biconditional statement always true?
Yes
What is a true statement that combines a true conditional statement and its true converse?
always true
What is a true statement that combines a true conditional statement and is its true converse?
always true
If you are hungry then you are not happy is assumed to be true is its converse If you are not happy then you must be hungry also always true?
No, it is not.
The converse and inverse of a conditional statement are logically equivalent?
This is not always true.
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.
What are some examples of a conditional statement?
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!)
If the statement If I am hungry then I am not happy is assumed to be true is its inverse If I am not hungry then I must be happy also always true?
No
Is the Converse of a false statement always false?
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 BF F T TF F T TT F F TF T T FLooking at the last two rows of the A and B columns, when either of the statements is false, its converse is true.
