Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements. If you study, then you will pass the test. If you pass the test, then you will pass the class.

If you study, then you will pass the class.

If you pass the test, then you should study.

If you pass the class, then you will pass the test.

If you study, then you will pass the test.

Do the following statements illustrate Law of Detachment or Law of Syllogism? If children under the age of 4 take Allergy medicine, then they can become very ill. 2 children in Little Pioneers ages 2 and 3 took Allergy medicine, then they became very ill.

The statements do not match either Law of Syllogism or Detachment.

Can the statement be written as a biconditional? "If a number is divisible by 2, then the number is even."

Yes. Biconditional would be "A number is divisible by 2 if and only if it is even.

Yes. Biconditional would be "If and only if a number if even, then it is divisible by 2."

No. The original conditional is not true.

Check the 2 statements that form the Biconditional of "A whole number is divisible by 3 if and only if the sum of the digits of the whole number is divisible by 3."

If a whole number is divisible by 3, then the sum of the digits of the whole number is divisible by 3.

If the sum of the digits is divisible by 3, then the whole number is divisible by 3.

If the sum of the digits are not divisible by 3, then the whole number is not divisible by 3.

If a whole number is not divisible by 3, then the digits of the whole number are not divisible by 3.

Is the statement "reversible"? "An isosceles triangle is a triangle with 2 congruent angles."

Yes, reversible because original statement and converse are both true.

Not reversible because both original statement and converse are both false.

Yes, reversible because original statement is true but converse is false.

Not reversible because original statement is true but converse is false.

Is the statement a "good definition"? "2 rays intersect if and only if they lie in the same plane."

No, because the converse is false.

No, because the original statement is false.

Yes, both original statement and converse are true.

Yes, because the key words "if and only if" are present.

Check all that apply about "Biconditionals".

Can write a biconditional when the original statement and the converse are both true.

Can write a biconditional when the original statement and the inverse are both true.

To write a biconditional, the key words are put in the beginning of the statement.

Can you make a conclusion? If so, state the Law. "If you like to snow ski, then you will like Colorado. If you like to wakeboard, then you will like Florida."

Yes, can make a conclusion using the Law of Syllogism.

Yes, can make a conclusion using Law of Detachment.

Yes, can make a conclusion by Law of Biconditional

If a polygon is a square, then it has exactly 4 congruent angles. If a polygon has exactly 4 congruent angles, then it is a rectangle. Conclusion, if possible?

If a polygon is a square, then it is also a rectangle. Law of Syllogism.

If a polygon is a square, then it is also a rectangle. Law of Detachment.

If polygon ABCD is a square, then it has 4 congruent angles and 4 congruent sides. Law of Detachment.

If a polygon is NOT a square, then it can have 4 congruent angles. Law of Syllogism.

Write the statement in "if/then" form. "Glass objects are fragile."

If an object is glass, then it is fragile.

If it is fragile, then it is made of glass.

If it is an object, then it is made of glass.

If it is fragile, then it can be broken easily.

Logic and Reasoning

Authored by Tara Puitz

Mathematics

9th - 11th Grade

CCSS covered

Used 10+ times

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20 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Underline the hypothesis and italicize the conclusion in each statement.

If your dog eats Purina, then he’ll stay happy and healthy.

If your dog eats Purina, then he’ll stay happy and healthy.

If your dog eats Purina, then he’ll stay happy and healthy.

If your dog eats Purina, then he’ll stay happy and healthy.

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.8

CCSS.RL.11-12.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

If a polygon is not a quadrilateral, then it is not a trapezoid.

If a polygon is not a trapezoid, then it is not a quadrilateral.

If a polygon is a trapezoid, then it is a quadrilateral.

A rectangle is also a quadrilateral.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the inverse of this statement?

If the polygon is not a quadrilateral, then it is not a trapezoid.

If the polygon is not a trapezoid, then it is not a quadrilateral.

If the polygon is a trapezoid, then it is a quadrilateral.

A rectangle is also a quadrilateral.

Tags

CCSS.HSG.CO.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

If a polygon is a trapezoid, then it is a quadrilateral.

If a polygon is not a quadrilateral, then it is not a trapezoid.

If a polygon is not a trapezoid, then it is not a quadrilateral.

A rectangle is also a quadrilateral.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is a counterexample of this statement?

Perpendicular Lines

An octagon

A hexagon

A rectangle

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The statement "an angle is a right angle if and only if its measure is 90^o" is an example of what type of statement?

Conditional

Conjecture

Biconditional

Tags

CCSS.8.G.A.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Using the Law of Detachment, draw a conclusion based on the statements given:
If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.

Sarah will get stuck in the security line.

Sarah will have a long flight.

Sarah will need to bring a neck pillow and headphones.

Sarah will get stuck with a middle seat on the plane.

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.8

CCSS.RL.11-12.1

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Logic and Reasoning

Underline the hypothesis and italicize the conclusion in each statement.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."What is the converse of this statement?

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."What is the inverse of this statement?

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."What is the contrapositive of this statement?

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."What is a counterexample of this statement?

The statement "an angle is a right angle if and only if its measure is 90o" is an example of what type of statement?

Using the Law of Detachment, draw a conclusion based on the statements given:If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.

Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements.If you study, then you will pass the test. If you pass the test, then you will pass the class.

Give the "truth value" of the following conditional statement:If an integer is negative, the square of it is positive.

Do the following statements illustrate Law of Detachment or Law of Syllogism?If children under the age of 4 take Allergy medicine, then they can become very ill.2 children in Little Pioneers ages 2 and 3 took Allergy medicine, then they became very ill.

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Popular Resources on Wayground

Discover more resources for Mathematics

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the inverse of this statement?

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is a counterexample of this statement?

The statement "an angle is a right angle if and only if its measure is 90^o" is an example of what type of statement?

Using the Law of Detachment, draw a conclusion based on the statements given:
If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.

Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements.

If you study, then you will pass the test. If you pass the test, then you will pass the class.

Give the "truth value" of the following conditional statement:
If an integer is negative, the square of it is positive.

Do the following statements illustrate Law of Detachment or Law of Syllogism?
If children under the age of 4 take Allergy medicine, then they can become very ill.
2 children in Little Pioneers ages 2 and 3 took Allergy medicine, then they became very ill.