Which statements are always true if the conditional statement is true?
Table of Contents
- 1 Which statements are always true if the conditional statement is true?
- 2 Can a conditional statement be either true or false?
- 3 When a compound statement is always true it is called a?
- 4 What types of statements are either both true or both false?
- 5 Is the converse of a false conditional is always false?
- 6 How do you prove a conditional statement is true?
- 7 What is the difference between true antecedent and material implication?
Which statements are always true if the conditional statement is true?
The contrapositive does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true.
What is a conditional statement that is false but has a true inverse?
Negating both the hypothesis and conclusion of a conditional statement. For example, the inverse of “If it is raining then the grass is wet” is “If it is not raining then the grass is not wet”. Note: As in the example, a proposition may be true but its inverse may be false.
Can a conditional statement be either true or false?
The important thing to remember is that the conditional statement P→Q has its own truth value. It is either true or false (and not both). Its truth value depends on the truth values for P and Q, but some find it a bit puzzling that the conditional statement is considered to be true when the hypothesis P is false.
Is the converse of a true statement always true or always false?
If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true….Example 1:
| Statement | If two angles are congruent, then they have the same measure. |
|---|---|
| Converse | If two angles have the same measure, then they are congruent. |
When a compound statement is always true it is called a?
A tautology is a compound statement that is always true.
Which of the following is always equivalent to the conditional statement?
A conditional statement is always logically equivalent to its contrapositive. We understand this from a example.
What types of statements are either both true or both false?
In general, when two statements are both true or both false, they are called equivalent statements. Just because a conditional statement and its contrapositive are both true does not mean that its converse and inverse are both false.
Is the converse always false?
The truth value of the converse of a statement is not always the same as the original statement. The converse of a definition, however, must always be true. If this is not the case, then the definition is not valid.
Is the converse of a false conditional is always false?
“If two angles are congruent, they are not equal.” this is a FALSE statement. Its converse is “If two angles are not equal, they are congruent.” The converse is also FALSE.
Why is the antecedent always true in a conditional statement?
Because the way a conditional statement is defined is such that only if The antecedent is True and the consequent false is the whole proposition false, this means, that all other pairings must be true . This follows because of the principle of bivalence.
How do you prove a conditional statement is true?
A conditional asserts that if its antecedent is true, its consequent is also true; any conditional with a true antecedent and a false consequent must be false. So For any other combination of true and false antecedents and consequents, the conditional statement is true ex : If I am thirsty, then I will drink a glass of water.
When do conditional statements sound illogical when p is false?
These conditional statements will then be true any time the hypothesis (“P”) is false, because “not P” will be true. If you are thinking of the sentence in English, as “If pigs can fly, then 2+2=8” it will seem illogical for the statement to be true (it always “sounds” illogical when P is false).
What is the difference between true antecedent and material implication?
If the antecedent (P) is true, then the material implication (->) holds only if the consequent (Q) is also true. That is, a true antecedent/premise/condition (P) can only imply a true /consequent/conclusion/consequence (Q). If the antecedent (P) is true and the consequent (Q) is false, then the implication does not hold (true).