Logic

Which of the following statements is the converse of

"If the moon is full, then the vampires are prowling.”

• If the vampires are prowling, then the moon is full.

• If the vampires are not prowling, then the moon is not full.

• If the moon is not full, then the vampires are prowling.

Which of the following statements is the inverse of

"If you do not understand geometry, then you do not know how to reason deductively."?

• If you reason deductively, then you understand geometry.

• If you understand geometry, then you reason deductively.

• If the do not reason deductively, then you understand geometry.

• If you understand geometry, then you do not know how to reason deductively.

Which of the following statements is the contrapositive of

"If you understand logic, you will be a good consumer."?

• If you are a good consumer, then you understand logic.

• If you are not a good consumer, then you do not understand logic.

• If you do not understand logic, then you will not be a good consumer.

• If you understand logic, you will not be a good consumer.

What is Logically Equivalent to  $L\rightarrow\sim K$  

•  $\sim L\rightarrow K$  

•  $K\rightarrow\sim L$  

•  $\sim L\vee K$  

•  $K\vee\sim L$  

Which of the following statements is logically equivalent to

"If you live in a mansion, then you have a big heating bill."?

• If you have a big heating bill, then you live in a mansion.

• If you do not live in a mansion, then you do not have a big heating bill.

• If you do not have a big heating bill, then you do not live in a mansion.

• If you live in a mansion, then you do not have a big heating bill.

 Use DeMorgan’s Law to draw a valid conclusion  $\sim\left(p\wedge\sim q\right)$  

•  $\sim p\vee q$  

•  $\sim p\wedge q$  

•  $p\vee\sim q$  

•  $p\wedge\sim q$  

Draw a valid conclusion and state the Law used:

 $\sim j\rightarrow\sim m$  

 $\sim j$  

• m, Disjunctive Inference

• ~m, Disjunctive Inference

• ~m, Law of Detachment 
  

• m, Law of Detachment 

From the two given statements, which is a valid conclusion and the Law used?
 $\sim p\vee\sim q$  
 $p$  

• ~q, Law of Detachment

• ~q, Disjunctive Inference 

• q, Law of Detachment

• q, Disjunctive Inference

Which Law is being used?

• DeMorgan's Law

• Law of Detachment

• Law of Contrapositive

• Chain Rule

Fill in the 3 missing Reasons "?"

• 3) Law of Detachment
  4) Disjunctive Inference
  6) DeMorgan's Law

• 3) Law of Detachment
  4) DeMorgan's Law
  6) Chain Rule

• 3) Law of Detachment
  4) DeMorgan's Law
  6) Disjunctive Inference

• 3) Law of Detachment
  4) Law of Contrapositive
  6) Disjunctive Inference