Logical Reasoning

Determine whether the sentence below is a statement or not a statement.

 $"x+3=5"$  

• Yes

• No

 $"\left\{2,5,7\right\}\cup\left\{prime\ numbers\right\}=\left\{2,5,7\right\}$  Determine whether the statement is true or false.

• True

• False

_________ circles has a radius of 18cm.

• All

• Some

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.

  $premise\ 1:\ All\ factors\ of\ 4\ are\ factors\ of\ 8$    $premise\ 2:\ 2\ is\ a\ factor\ of\ 4$ 
 $conclusion:$  ______________________

 Complete the argument to form valid and sound deductive argument.

Given the surface are of a cone $=\pi r\left(r+s\right),$  make a conclusion by deduction for the surface area of the five similar cones such that r=7cm and s=13cm.

•   $Surface\ area\ of\ five\ cones\ is\ 700\pi$  

•  $Surface\ area\ of\ five\ cones\ is\ 140\pi$  

•  $Surface\ area\ of\ five\ cones\ is\ 540\pi$  

•  $Surface\ area\ of\ five\ cones\ is\ 1080\pi$  

 $premise\ 1:\ Mas\ got\ A+\ for\ Mathematic$     $premise\ 2:\ Yazmeen\ got\ A+\ for\ Mathematic$    $premise\ 3:\ Amna\ got\ A+\ for\ Mathematic$    $conclusion:\ All\ students\ in\ 4E\ got\ A+\ for\ Mathematic\$  Determine whether the given argument are strong or weak, and cogent or not cogent.

• Strong and cogent

• Strong and not cogent

• Weak and cogent

• Weak and not cogent