# Is the converse of a statement true?

Space and AstronomyIf the statement is true, then the contrapositive is also logically true. **If the converse is true, then the inverse is also logically true**.

…

Converse, Inverse, Contrapositive.

Statement | If p , then q . |
---|---|

Converse | If q , then p . |

Inverse | If not p , then not q . |

Contrapositive | If not q , then not p . |

## Are converse of false statements true?

If p is TRUE, and q is FALSE, then p⟹q is FALSE. And the converse, **q⟹p, is TRUE**. “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.

## Is the converse of a theorem always true?

Additionally, the actual theorem can also be the converse of the converse theorem; they are converses of each other. However, **not all converses are true, even if the original statement is true**.

## What is a converse of a statement?

The converse of a statement is **formed by switching the hypothesis and the conclusion**. The converse of “If two lines don’t intersect, then they are parallel” is “If two lines are parallel, then they don’t intersect.” The converse of “if p, then q” is “if q, then p.”

## How do you prove false converse?

Video quote: *So quadrilateral is a four-sided figure this quadrilateral has all four sides equal we are going to prove that this is a parallelogram of course it looks like a parallelogram.*

## What is the equivalent truth value of a converse statement?

A conditional statement is logically equivalent to **its contrapositive**. Converse: Suppose a conditional statement of the form “If p then q” is given. The converse is “If q then p.” Symbolically, the converse of p q is q p.

## How does a converse relate to the original statement?

The converse is **logically equivalent to the inverse of the original conditional statement**.

## What is converse conditional statement?

Definition: The converse of a conditional statement is **created when the hypothesis and conclusion are reversed**. In Geometry the conditional statement is referred to as p → q. The Converse is referred to as q → p.

## What is converse in discrete mathematics?

In logic and mathematics, the converse of a categorical or implicational statement is **the result of reversing its two constituent statements**. For the implication P → Q, the converse is Q → P.

## When the original statement and converse are both true?

Vocabulary

Term | Definition |
---|---|

biconditional statement | A statement is biconditional if the original conditional statement and the converse statement are both true. |

Conditional Statement | A conditional statement (or ‘if-then’ statement) is a statement with a hypothesis followed by a conclusion. |

## How do you write converse?

Video quote: *So that's the conditional statement to write the converse need to recall that the converse is the reverse of the conditional statement if Q. And then P.*

## What is the converse of the statement if two angles are right angles then the angles are congruent?

If two angles have the same measure, then they are congruent. Examples: Statement: If 2 angles are right angles, then they are congruent. Converse: **If 2 angles are congruent, then they are right angles**.

## What is the converse of the conditional statement if two angles are congruent?

It follows that the converse statement, “**If two angles are congruent, then the two angles have the same measure**,” is logically equivalent to the inverse statement, “If two angles do NOT have the same measure, then they are NOT congruent.”

## What is the converse of the statement if it is a vertical angle then they are congruent?

To make the converse, make the conclusion the hypotheses and the hypothesis the conclusion. **If two angles are vertical angles, then the angles are congruent**. Note: The original statement is false! The converse is true.

## What is the converse of the statement if Bob does his homework then George gets candy?

If the Sun rises in the west, then it sets in the east. 13 What is the converse of the statement “If Bob does his homework, then George gets candy”? **If George gets candy, then Bob does his homework.**

## What is the inverse of the statement if it is sunny I will go swimming?

What is the inverse the following statement: “If it is sunny, I will go swimming.” **If it is not sunny, then I will go swimming**. If I go swimming, then it is sunny.

## Which statement is logically equivalent to if it is warm then I go swimming?

CONVERSE: If I am a New Yorker, then I live in Albany. CONTRAPOSITIVE: If I am not a New Yorker, then I do not live in Albany. The contrapositive is logically equivalent.

1) | If I go swimming, then it is warm. |
---|---|

3) | If I do not go swimming, then it is not warm. |

4) | If it is not warm, then I do not go swimming. |

## What is the definition of Contrapositive in geometry?

: **a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them** “if not-B then not-A ” is the contrapositive of “if A then B “

## What does converse mean in logic?

converse, in logic, **the proposition resulting from an interchange of subject and predicate with each other**. Thus, the converse of “No man is a pencil” is “No pencil is a man.” In traditional syllogistics, generally only E (universal negative) and I (particular affirmative) propositions yield a valid converse.

## What is the contrapositive of a converse statement?

If the statement is true, then the contrapositive is also **logically true**. If the converse is true, then the inverse is also logically true.

Converse, Inverse, Contrapositive.

Statement | If p , then q . |
---|---|

Converse | If q , then p . |

Inverse | If not p , then not q . |

Contrapositive | If not q , then not p . |

## What kind of statement can be made if a conditional statement and its converse are both true?

Biconditional

If a conditional and its converse are both true, we can write it as **a Biconditional** using if and only if. Biconditional Two lines intersect iff their intersection is exactly one point.

## What is a false converse?

Switching the hypothesis and conclusion of a conditional statement. For example, the converse of “If it is raining then the grass is wet” is “If the grass is wet then it is raining.” Note: As in the example, **a proposition may be true but have a false converse**.

## Which conditional has the same truth value as its converse?

The inverse

**The inverse** always has the same truth value as the converse. We could also negate a converse statement, this is called a contrapositive statement: if a population do not consist of 50% women then the population do not consist of 50% men. The contrapositive does always have the same truth value as the conditional.

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