Implication (Logical Reasoning)

Which is the converse of:
"If a figure is a circle with radius r, then its circumference in 2(pi)r."

• If a figure has a circumference of 2(pi)r, then its a circle with radius r.
• If a figure doesn't have a circumference, then it's a circle with a radius of r.
• If a figure isn't a circle with radius r, then its circumference isn't 2(pi)r
• If a figure isn't a circle, then it doesn't have a circumference.

Contrapositive of:
If an integer ends with 0, then it's divisible by 2.

• If an integer ends with 2 then it's divisible by 0.
• If an integer doesn't end in 0, then it's not divisible by 2.
• If an integer isn't divisible by 2, then it's doesn't end in 0.
• If an integer is divisible by 2, then it ends with 0.

choose two implications based on the following statement.

y > 3 if and only if 2y > 6

• If y > 3, then 2y > 6

• If y < 6 , then 2y > 6

• If 2y > 6, then y > 3

• If 2y > 6, then y < 6

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.

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.

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

• If I do not have a Siberian Husky, then I do not have a dog.
• If I have a dog, then I have a Siberian Husky.
• If I do not have a dog, then I do not have a Siberian Husky.
• If I do not have a Siberian Husky, then I have a dog. 

Determine the antecedent and consequent of the statement:
"If the perimeter of a rectangle A is 2(x+y), then the area of rectangle is xy."

• Antecedent: The area of rectangle A is xy
  Consequent: Perimeter of rectangle A is 2(x+y)

• Antecedent: The area of rectangle A is xy
  Consequent: Perimeter of rectangle A is 2x+y

• Antecedent: Perimeter of rectangle A is 2x+y
  Consequent: The area of rectangle A is xy

• Antecedent: Perimeter of rectangle A is 2(x+y)
  Consequent: The area of rectangle A is xy

Write an appropriate implication based on the following pairs of implications:

a) If x is a multiple of 10, then x is a multiple of 5.

b) if x is a multiple of 5, then x is a multiple of 10.

 $"20\%\ of\ 30\ is\ 6\ if\ and\ only\ if\ 0.2\times30=6."$  Construct two appropriate implications based on the implication.

•  $p:\ 20\%\ of\ 30\ is\ 6$   $q:\ 0.2\times30=6$  

•  $p:\ 0.2\times\times30=6$   $q:\ 20\%\ of\ 30\ is\ 6$  

•  $\left(a\right)\ If\ 20\%\ of\ 30\ is\ 6,\ then\ 0.2\times30=6$   $\left(b\right)\ If\ 0.2\times30=6,\ then\ 20\%\ of\ 30\ is\ 6$  

•  $\left(a\right)\ If\ 0.2\times30=6,\ then\ 20\%\ of\ 30\ is\ 6$   $\left(b\right)\ If\ 20\%\ of\ 30\ is\ 6,\ then\ 0.2\times30=6$  

 $"If\ w>20,\ then\ w>30."$  

Find the contrapositive for the statement and decide if it is a true or false statement.

•  $if\ w\le20,\ then\ w\le30.$  True.

•  $if\ w>30,\ then\ w>20.$  False.

•  $if\ w\ge20,\ then\ w\ge30.$  True.

•  $if\ w\le30,\ then\ w\le20.$  False.