Mathematics (logical reasoning - Arguments)

An argument consists of sets of statements which are called premises and a conclusion is made based on these premises

• True

• False

Which statement is a valid conclusion based on the argument?
If a polygon is a regular pentagon, then the polygon has exactly five congruent angles.
The polygon is a regular pentagon.

• The polygon is a rectangle.
• The polygon is a regular quadrilateral.
• The polygon has exactly five congruent angles.
• The polygon has congruent sides.

Determine whether the following deductive argument is valid or not. Hence, determine whether the argument is sound or not.

Premise 1: All negative numbers are less than zero
Premise 2:  $a$  is a negative number 

Conclusion:  $a$  is less than zero 

• valid and sound 

• valid but not sound 

• not valid but sound 

• not valid and not sound 

Complete the following valid deductive argument with the correct conclusion

Premise 1: If m is an even number, then m+1 is an odd number

Premise 2: 7+1 is not an odd number

Conclusion:

• 7 is an even number

• 7 is not an odd number

• 7 is not an even number

Based on the information below, form a conclusion deductively for the surface area of a sphere with a radius of 9cm.
' The surface area of a sphere with radius j is  $4\pi j^2$  '

• The surface area of a sphere with a radius of 9cm is  $4\pi j^2=324\pi^2$  

• The surface area of a sphere with radius j is  $4\pi j^2$  

• The surface area of a sphere  is  $4\pi\left(9\right)^2=324\pi^2$ 

• The surface area of a sphere with a radius of 9cm is  $4\pi\left(9\right)^2=324\pi^2$ 

Write Premise 2 to complete the following argument

Premise 1: If x is an odd number, then x cannot be divided completely by 2

Premise 2:

Conclusion: 24 is not an odd number

• 24 can be divided completely by 2

• 24 can be divided completely by 3

• 48 can be divided completely by 2

• 24 can't be divided completely by 2

The strenght of an inductive argument is based on the level of truth of the conclusion with assumption that all premises are true.

• True

• False

Write a logical conclusion.

I am going to the store or I am going home

I did not go to the store

Write a logical conclusion

If I am 7 feet tall, then I am over 5ft tall.

I am not over 5ft tall.

Is this argument valid or invalid, and why?

If you are traveling at 50mph, then you are in a car.

You are not traveling at 50mph.

Therefore, you are not in a car.

• Valid, fallacy of inverse.

• Invalid, fallacy of inverse.

• Valid, fallacy of converse.

• Invalid, fallacy of converse.