Laws of Logic

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

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If x = 2, then 2x – 10 = –6.
Statement 2: x = 2 

• 2x – 10 = –6 
• x = 2
•  If 2x – 10 = –6, then x = 2
• not possible 

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, therefore

• 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.

Tags

CCSS.L.4.1C

CCSS.L.9-10.1B

Which law of deductive reasoning is being used, if any?
If a triangle is equilateral, then all three sides are congruent. 
If all the sides of a triangle are congruent, then the angles opposite them are congruent. 
Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

• Law of Detachment
• Law of Syllogism
• Law of the Contrapositive
• Not valid

Which law of logic is this:
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.

• Law of Detachment
• Law of Contrapositive
• Law of Syllogism
• Law of Biconditional

Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.

• If the measures of the angles are equal, then the angles are congruent.
• "If angles are not congruent, then the measures of the angles are not equal."
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

Given, "If angles are congruent, then the measures of the angles are equal." Identify the inverse.

• If the measures of the angles are equal, then the angles are congruent.
• "If angles are not congruent, then the measures of the angles are not equal."
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

Tags

CCSS.HSG.CO.C.9

Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.

• If the measures of the angles are equal, then the angles are congruent.
• If angles are not congruent, then the measures of the angles are not equal.
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

Tags

CCSS.8.G.A.2

Given, "If angles are congruent, then the measures of the angles are equal." Identify the hypothesis.

• The measures of the angles are equal.
• Angles are congruent.
• the measures of the angles are equal.

Given, "If angles are congruent, then the measures of the angles are equal." Identify the conclusion.

• If the angles are congruent.
• The angles are congruent.
• Then the measures of the angles are equal.
• The measures of the angles are equal.

Tags

CCSS.7.G.B.5