A biconditional that combines p → q a n d q → p p\rightarrow q\ and\ q\rightarrow p p → q a n d q → p is ...

p ↔ q p\leftrightarrow q p ↔ q

∼ p → ∼ q \sim p\rightarrow\sim q ∼ p → ∼ q

∼ q → ∼ p \sim q\rightarrow\sim p ∼ q → ∼ p

Test the statement below to see if it is reversible. If so, write it as a biconditional. Complementary angles are two angles with measures that have a sum of 90.

Reversible; Two angles are complementary if and only if the sum of their measures is 90.

Reversible; If two angles are complementary, then the sum of their measures is 90.

Is the statement below a good definition? If not, explain. A cat is an animal with whiskers.

Not good: The statement is not reversible.

Not good: The statement uses vague terms.

Not good: The statement uses terms that are not clearly understood.

Which two conditional statements form this biconditional? A polygon is a triangle if and only if it has exactly three sides.

If a polygon has exactly three sides, then it is a triangle.

If a polygon is a triangle, then it has exactly three sides.

A polygon is a triangle if and only if it has exactly three sides.

A polygon has exactly three sides.

Which conditional has the same truth value as its converse?

If an angle has a measure of 80, then it is acute.

If x = 7 x=7 x = 7 then ∣ x ∣ = 7 \left|x\right|=7 ∣ x ∣ = 7 .

If a figure is a square, then it has four sides.

Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If a point is a midpoint, then it divides the segment into two congruent segments. If a point divides a segment into two congruent segments, then it is a midpoint.

Both statements are true. A point is a midpoint if and only if it divides a segment into two congruent segments.

Both statements are true. A point is a midpoint if it is in the middle.

One statement is false. If a point is a midpoint, it may not divide the segment equally.

One statement is false. If a point divides a segment into two congruent segments, then it is called a lateral point.

2.3 Biconditionals and Definitions

Authored by Donna Legg-Battles

Mathematics

9th - 10th Grade

CCSS covered

Used 19+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When a conditional statement and its converse are true, you can combine them as a true ?.

hypothesis

counterexample

unconditional

biconditional

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A biconditional may be written using the phrase...

if-then

if and only if

not if but then

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The converse of the statement p→q is...

$\sim p\rightarrow\sim q$

$p\leftrightarrow q$

$q\rightarrow p$

$\sim q\rightarrow\sim p$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A biconditional that combines $p\rightarrow q\ and\ q\rightarrow p$ is ...

$\sim p\rightarrow\sim q$

$p\leftrightarrow q$

$q\rightarrow p$

$\sim q\rightarrow\sim p$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A good definition may be rewritten as a(n) ? statement.

biconditional

inverse

contrapositive

Which statement is a counterexample for the following conditional?
If you live in Decatur, then you live in Alabama.

John Smith lives in Montgomery, Alabama.

Carson Wilson lives in Hartselle, Alabama.

Mary Jones lives in Decatur, Georgia.

Susie Sams lives in Decatur.

What is the converse of the statement:
"If a number is divisible by 20, then it is even."

A number divisible by 20 is even.

If a number is even, then it is divisible by 20.

If a number is not divisible by 20, then it is not even.

If a number is not even, then it is not divisible by 20.

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2.3 Biconditionals and Definitions

When a conditional statement and its converse are true, you can combine them as a true ?.

A biconditional may be written using the phrase...

The converse of the statement p→q is...

A biconditional that combines $p\rightarrow q\ and\ q\rightarrow p$ is ...

A good definition may be rewritten as a(n) ? statement.

Which statement is a counterexample for the following conditional?
If you live in Decatur, then you live in Alabama.

What is the converse of the statement:
"If a number is divisible by 20, then it is even."

What is the truth value of the converse of:
"If a number is divisible by 20, then it is even."

Which is a counterexample for the following conditional:
If an electronic device has a screen then it is a television.

What is the converse of the statement:
"If x = 12, then 2x - 5 = 19"

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2.3 Biconditionals and Definitions

When a conditional statement and its converse are true, you can combine them as a true __?__.

A biconditional may be written using the phrase...

The converse of the statement p→q is...

A biconditional that combines p→q and q→pp\rightarrow q\ and\ q\rightarrow pp→q and q→p is ...

A good definition may be rewritten as a(n) __?__ statement.

Which statement is a counterexample for the following conditional?If you live in Decatur, then you live in Alabama.

What is the converse of the statement: "If a number is divisible by 20, then it is even."

What is the truth value of the converse of:"If a number is divisible by 20, then it is even."

Which is a counterexample for the following conditional:If an electronic device has a screen then it is a television.

What is the converse of the statement:"If x = 12, then 2x - 5 = 19"

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

When a conditional statement and its converse are true, you can combine them as a true ?.

A biconditional that combines $p\rightarrow q\ and\ q\rightarrow p$ is ...

A good definition may be rewritten as a(n) ? statement.

Which statement is a counterexample for the following conditional?
If you live in Decatur, then you live in Alabama.

What is the converse of the statement:
"If a number is divisible by 20, then it is even."

What is the truth value of the converse of:
"If a number is divisible by 20, then it is even."

Which is a counterexample for the following conditional:
If an electronic device has a screen then it is a television.

What is the converse of the statement:
"If x = 12, then 2x - 5 = 19"