Answer Expert Verified. 1)
The fourth statement
is not a good definition. Because it is not sufficient that the ray splits the angle into two angles, it is necessary that the two angles are equal.
Which biconditional is not good definition?
If
three points are collinear
, then they are coplanar. If three points are coplanar, then they are collinear. The biconditional is not a good definition. Three coplanar points might not lie on the same line.
What biconditional is a good definition?
: a relation between
two propositions that is true only when both propositions
are simultaneously true or false — see Truth Table.
Are all definitions biconditional?
A biconditional statement can be either true or false. To be true, both the conditional statement and its converse must be true. This means that a true biconditional statement is true both “forward” and “backward.”
All definitions can be written as true biconditional statements
.
Do biconditional statements have to be true?
If conditional statements are one-way streets, biconditional statements are the two-way streets of logic.
Both the conditional and converse statements must be true to produce a
biconditional statement: Conditional: If I have a triangle, then my polygon has only three sides.
Is the following statement a good definition explain a square is a figure with four right angles?
No since rectangles also have four right angles. A good definition would be
“Squares have four right angles and four congruent sides
.”
Which statement is the converse of if a figure is a triangle then it has three sides?
Converse: If a figure has three sides, then
it is a triangle
. Inverse: If a figure is not a triangle, then it does not have three sides.
What is a true biconditional statement?
A biconditional statement is a
statement combing a conditional statement with its converse
. So, one conditional is true if and only if the other is true as well. It often uses the words, “if and only if” or the shorthand “iff.” It uses the double arrow to remind you that the conditional must be true in both directions.
What is a Contrapositive example?
Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of “
If it is raining then the grass is wet”
is “If the grass is not wet then it is not raining.”
Can a biconditional statement be false?
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 is converse in math?
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. For the categorical proposition All S are P, the converse is All P are S.
What can be written as a biconditional statement?
‘ Biconditional statements are true statements that combine the hypothesis and the conclusion with the key words ‘
if and only if
. ‘ For example, the statement will take this form: (hypothesis) if and only if (conclusion). We could also write it this way: (conclusion) if and only if (hypothesis).
What is the symbol for if and only if?
| Symbol Name Read as | ⇔ ≡ ⟷ material equivalence if and only if; iff; means the same as | ¬ ̃ ! negation not | Domain of discourse Domain of predicate | ∧ · & logical conjunction and |
|---|
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”)
.
What is biconditional equivalent to?
If p and q are two statements then “p if and only if q” is a compound statement, denoted as
p ↔ q
and referred as a biconditional statement or an equivalence. The equivalence p ↔ q is true only when both p and q are true or when both p and q are false.
