Conditional Statement

Question 1

What do we know about sufficient factors in conditional statements?

Answer 1

The sufficient factor is the active part of a conditional statement that triggers the necessary part.

It is something that is enough by itself to guarantee a result; however, they are not always required in otrder to achieve the result.

• It is found on the left side of the arrow in a conditional statement.
• It may be indicated by the following words:
  
  • **All **
  • Every
  • Whenever
  • No
    
    • No cats are kind: C→~kind
    • No Jets are Sharks: Jets → ~Sharks
    • None of the Jets are Sharks: Jets →~Sharks
      
      • If you are a member of the Jets, then you definitely are not a member of the Sharks.
  • If
  • UNLESS: indicates a sufficient condition about the results when something does not occur

You can’t be president unless you are a citizen: ~citizen→~president

In a case like this, translate unless to “if not.” That will make the “if” more noticeable.

You can’t be president if not you are a citizen (if you are not a citizen).

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Question 2

What do we know about necessary factors in conditional statements?

Answer 2

If they are not there, then an outcome cannot occur. However, it does not guarantee the result by itself.

• They are found on the right side of the arrow
• Linguistically, they are identified by:
  
  • Only if (whatever follows it is necessary)
  • Cannot…unless (what comes after unless is necessary)

Question 3

All cows are mammals.

Every cow is a mammal.

In an animal is a cow, then it is also a mammal.

An animal is a mammal if it is a cow.

Whenever you see a cow, you’re seeing a mammal.

Answer 3

All have the same diagram:

cow → mammal

~mammal→ ~cow

Question 4

Only the well-dressed are permitted to attend.

you will be permitted to attend only if you are well-dressed.

Only if you are well-dressed will you be permitted to attend.

Answer 4

All have the same diagram:

permitted to attend → well-dressed

~well-dressed → ~permitted to attend

Question 5

You will not be permitted to attend unless you are well-dressed.

You will not be permitted to attend if not you are well dressed

Answer 5

Take the two statements, put one on each side of the arrow, and negate the one in front of the arrow

~well-dressed → ~permitted to attend

permitted to attend → well-dressed

Question 6

I will not take a walk and I will not clean house.

Answer 6

I will neither walk nor clean house.”

If the seminar is attended by neither Fred nor Jenny, then it will also not be attended by Joe.

~Fred and ~Jenny → ~Joe

Joe → Fred or Jenny

Question 7

What about statements containing the quantity “no?”

No A are B.

No jets are sharks.

None of the A are B.

None of the jets are sharks.

Answer 7

Place one statement on each side of the arrow, and negate the statement to the right of the arrow:

A → ~B

Sharks are not jets.