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## What is the converse of obtuse angles have measures more than 90?

Conditional – If an angle is obtuse, then it measures more than 90 degrees. Converse – If an angle measures more than 90 degrees, then it is obtuse.

## Does the statement angles that measure more than 90 degrees are obtuse angles have a counterexample?

Answer is “True”. A counterexample is any angle 180 deg or greater. An obtuse angle is an angle whose measure is between 90 deg and 180 deg.

## Is 90 degrees obtuse or acute?

Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.

## What is the Contrapositive of if an angle is obtuse then its measure is 150?

CONVERSE – If an angle measures 150°, it is obtuse. INVERSE – If an angle is not obtuse, then it does not measure 150°. CONTRAPOSITIVE – If an angle does not measure 150°, it is not obtuse.

## What is if/then form?

A conditional statement (also called an If-Then Statement) is a statement with a hypothesis followed by a conclusion. Another way to define a conditional statement is to say, “If this happens, then that will happen.” Keep in mind that conditional statements might not always be written in the “if-then” form.

## What is the Contrapositive of the statement if the measure of an angle is less than 90 ∘ 90 ∘ then the angle is acute?

negates both the hypothesis and conclusion. Swithces the hypothesis and conclusion and negates both. What is the contrapositive of this statment: If an angle measure is less than 90°, then then it is an acute angle.

## What is the converse of if an angle measures 90 degrees?

A conditional statement with a true converse could be “If an angle is right, then it is 90 degrees.” The converse would be “If an angle is 90 degrees, then it is right.” This is true.

## What is the converse of the statement if an angle is a right angle then it measures 90 degrees?

Consider the following statements: Conditional Statement: If an angle measures 90 degrees, then it is a right angle. – TRUE. Converse Statement: If an angle is a right angle, then it measures 90 degrees.

## What is the IF THEN form of the following statement an acute angle measures less than 90 degrees?

Answer Expert Verified The correct statement is C. If an angle is an acute angle, then the angle measures less than 90 degrees.

## What is the converse and the truth value of the converse of the following conditional If an angle is a right angle then its measure is 90?

What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then its measure is 90. a. If an angle is not a right angle, then its measure is 90.

## When can a Biconditional statement be true?

Definition: A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a double-headed arrow . The biconditional p q represents “p if and only if q,” where p is a hypothesis and q is a conclusion.

## What Biconditional statement is true?

The biconditional statement p⇔q is true when both p and q have the same truth value, and is false otherwise. A biconditional statement is often used in defining a notation or a mathematical concept.

## What are the three main logical connectives?

Commonly used connectives include “but,” “and,” “or,” “if . . . then,” and “if and only if.” The various types of logical connectives include conjunction (“and”), disjunction (“or”), negation (“not”), conditional (“if . . . then”), and biconditional (“if and only if”).

## Can you negate a quantifier?

To negate a sequence of nested quantifiers, you flip each quantifier in the sequence and then negate the predicate. So the negation of ∀x ∃y : P(x, y) is ∃x ∀y : P(x, y) and So the negation of ∃x ∀y : P(x, y) and ∀x ∃y : P(x, y). Again, after some thought, this make sense intuitively.

## What is the negation of P and Q?

Negation of a Conditional By definition, p → q is false if, and only if, its hypothesis, p, is true and its conclusion, q, is false. It follows that the negation of “If p then q” is logically equivalent to “p and not q.”

## Why are P and Q used in logic?

The propositions are equal or logically equivalent if they always have the same truth value. That is, p and q are logically equivalent if p is true whenever q is true, and vice versa, and if p is false whenever q is false, and vice versa. If p and q are logically equivalent, we write p = q.

## What does P -> Q mean?

The statement “p implies q” means that if p is true, then q must also be true. The statement “p implies q” is also written “if p then q” or sometimes “q if p.” Statement p is called the premise of the implication and q is called the conclusion.

## What is an example of an implication?

The definition of implication is something that is inferred. An example of implication is the policeman connecting a person to a crime even though there is no evidence. The act of implying or the condition of being implied. An implicating or being implicated.

## What is imply in math?

“Implies” is the connective in propositional calculus which has the meaning “if is true, then is also true.” In formal terminology, the term conditional is often used to refer to this connective (Mendelson 1997, p. 13). The symbol used to denote “implies” is , (Carnap 1958, p.

## Can the converse be true?

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.

## Which is the inverse of P → Q quizlet?

If p = a number is negative and q = the additive inverse is positive, the original statement is p → q. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.

2020-12-24