Deductive Reasoning

________, also known as logical reasoning, is the process of reasoning logically from given statements or facts to a conclusion.

• Inductive Reasoning

• Deductive Reasoning

• Biconditional Statements

• Contrapositive statements

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3)  ???????
What belongs in line 3?

• Figure A is a polygon.
• Figure A is a circle.
• Figure A is a square.
• invalid; nothing belongs in line 3

Tags

CCSS.HSG.CO.A.1

If an angle measures 40⁰, then the angle is acute.
 $m\angle A=40$  
What is the logical conclusion?

• ∠A is complementary to ∠B

• ∠A is acute.

• ∠A is obtuse.

• ∠A is 40⁰

Tags

CCSS.HSG.CO.A.1

Make a conclusion.

1. If a number is divisible by 10, then it is divisible by 2.

2. If a number is divisible by 2, then it is even.

• If a number is divisible by 10, then it is even,

• If a number is even, then it is divisible by 10.

• If a number is divisible by 2, then it is even.

• If a number is even, then it is divisible by 2.

Tags

CCSS.HSA.REI.A.1

Make a conclusion.

1. If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
2. If the length of a side of a square is 5 ft, then the area is 25 ft².

• If the side of a square is 5 ft, then the perimeter is 20 ft.

• If the perimeter of a square is 20 ft, then the area is 25 ft²

• If the area of a square is 25 ft², then the side length is 5 ft.

• If the are of a square is 25 ft², then the perimeter is 20 ft.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

Write the conditional 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.

Tags

CCSS.HSS.CP.A.3

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

• If Tom goes fishing then he catches a fish.
• If Tom brings his pole then he goes fishing
•  If Tom catches a fish then he brought his pole.
• If Tom brings his pole then he catches a fish.

Determine if the conjecture is valid.

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.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

IF All even numbers are divisible by 2

AND 28 is even

THEN

• 2 is an even number

• 28 is divisible by 2

• All numbers are divisible by 2

• All numbers are even numbers

IF an apple a day keeps the doctor away.

AND Joe ate an apple every day.

THEN

• He will get a stomach ache

• This makes no sense, what do apples have to do with doctors?

• Joe will be spending lots of time at the dentists office

• The doctor will stay away