GM 02.3 Deductive Reasoning

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...

• Look out for the snowplows while driving to school.
• The big test will not be given today.
• The roads will be hard to drive on.
• You should call the school to see if school is canceled.

Which is a valid conclusion from these statements?
If a quadrilateral is a rhombus, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

• Opposite angles of a quadrilateral are congruent
• Opposite angles of a rhombus are congruent
• Every quadrilateral is a rhombus
• Every parallelogram is a rhombus

Tags

CCSS.HSG.CO.C.11

(1) If you drive safely, then the life you save may be your own.
(2) AJ drives safely.
(3)  The life AJ saves may be his own.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Detachment
• Law of Syllogism
• Law of Contrapositive
• invalid

p→q
q→r
∴p→r
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

p→q
p
∴q
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Write the if-then statement that follows from the pair of true statements. If the sun is shining, then it is a beautiful day.  If it is a beautiful day, then we will have a picnic.

• If the sun is shining, then it is a beautiful day.
• If it is a beautiful day, then the sun is shining.
• If the sun is shining, then we will go on a picnic.
• If we go on a picnic, then the sun is shining.

Determine if the conjecture is valid by the Law of Syllogism.
Given: If you are in California, then you are in the west coast. If you are Los Angeles, then you are in California.
Conjecture: If you are in Los Angeles, then you are in the west coast.

• No, the conjecture is not valid.
• Yes, the conjecture is valid.

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If I study for one hour each day, then I will score well on the exam
Statement 2: I will score well on the exam

•  I study for 1 hour each day.
• I do not study for 1 hour each day
• If I do well on the exam, I studied for 1 hour each day.
• not possible

What is a valid counterexample for the following statement? "If an animal is a panther, then it lives in the forest."

• It lives in a zoo.
• No counterexample, this is true.
• It lives in an aquarium.
• It is a monkey

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RI.8.8

Which of the following is a biconditional statement?

• If you do not vote, then you are not at least 18 years old.
• You can vote if and only if you are 18 years old.
• If you are 18 years old, then you can vote.