chapter 3: logical reasoning

Which of the following is a statement?

• $y>5$

• $6+x=2$

• 5 is a factor of 15.
  

• what is the total of 5 and 8?
  

Which of the following statements is true?

• $5\times2=5^2$

• $2^0=0$

• $11<7$

• $10_2=2_{10}$

which of the following is a false statement?

• $5^2=10\ or\ 4\div8=2$

• $8+9=17\ and\ 8\times4=32$

• Some pyramids have a square base.
  

• All multiples of 6 are multiples of 3.
  

" If   $m=-7$  , then   $m^2=49$  ".

State the antecedent in the above implication.

•  $m=-7$  

•  $m=7$  

•  $m^2=-49$  

•  $m^2=49$  

"If  $x=144,$  then  $\sqrt{x}=12$  "

State the inverse of the above implication.

•  $If\ \sqrt{x}=12,\ then\ x=144.$  

•  $If\ \sqrt{x}\ne12,\ then\ x\ne144.$  

•  $If\ x\ne144,\ then\ \sqrt{x\ }=12.$  

•  $If\ x\ne144,\ then\ \sqrt{x}\ne12.$  

Premise 1:  $If\ x>10,\ then\ x^2>100.$ 

Premise 2:  $15>10$ 

Make a conclusion based on the two given premises.

•  $15^2>10$  

•  $15^2>100$  

•  $15^2<10$  

•  $15^2<100$  

All acute angles are less than  $90\degree$  .  $\angle KLM\ is\ an\ acute\ angle.$ 

State the conclusion for the above deductive argument.

•  $\angle KLM=90\degree$  

•  $\angle KLM>90\degree$  

•  $\angle KLM<90\degree$  

•  $\angle KLM\ge90\degree$  

Given the implication "  $If\ \theta=60\degree,\ then\ \cos\theta=\frac{1}{2}$  ."

The inverse of this implication is

•  $If\ \cos\theta=\frac{1}{2},\ then\ \theta=60\degree$  

•  $If\ \theta\ne60\degree,\ then\ \cos\ \theta\ne\frac{1}{2}$  

•  $If\ \cos\theta\ne\frac{1}{2},\ then\ \theta\ne60\degree$  

•  $If\ \theta\ne60\degree,\ then\ \cos\ \theta=\frac{1}{2}$  

Premise 1: $If\ x\ is\ a\ negative\ integer,\ then\ \sqrt{x}is\ not\ defined.$  Premise 2:

Conclusion: $\sqrt{-8}\ is\ not\ defined.$ 

Premise 2 is

•  $-8\ is\ a\ negative\ integer$  

•  $\sqrt{-8}\ is\ a\ negative\ integer.$  

•  $-8\ is\ not\ a\ negative\ integer.$  

•  $\sqrt{-8}is\ not\ a\ negative\ integer.$  

Premise 1:  $All\ factors\ of\ 21\ are\ odd\ numbers.$ 

Premise 2:  $7\ is\ an\ odd\ number.$ 

Conclusion:  $7\ is\ a\ factor\ of\ 21.$ 

The above deductive argument is

• valid and sound
  

• valid but not sound
  

• not valid but sound
  

• not valid and not sound