If 'some women are writers' is true, which of the following codes are CORRECT A. 'All women are writers' false B. 'All women are writers' is true C. 'No women are writers' is false D. 'Some women are not writers' is undetermined Choose the correct answer from the options given below:?

LohaHridoy
  1.  A and B only
  2. B and C only
  3. C and D only
  4. B and D only

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AhmedNazir

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Option 3 : C and D only

The square of opposition is a diagram used in categorical logic to depict the logical relationship that exists between particular propositions based on their form.

 

Diagram of Aristotelian Square of Opposition. 

The four corners of this diagram represent the four basic forms of propositions. 

 Propositions From   Title  Example
A All S is P Universal affirmatives All women are writers. 
E No S are P Universal negative No women are writers.
I Some S are P Particular affirmatives Some women are writers. 
O Some S are not P Particular Negative Some women are not writers.

Now applying the rule of the Square of Opposition.

Types of Square of Opposition  Rules
Contradictory

A and O, E, and I propositions are contradictory. 
If One is True the other will be false definitely.

If One is False the other will be True definitely. 

For Example, Some women are writers(I) is True then, No women are writers (E) must be False 
Contrary

A and E propositions are contrary. 

It's always Between Universal. 

Both statements cannot be true at the same time but both can be False. 

If One is True the other will be False definitely. 

If One is False the other will be  Doubtful. 
Sub-contrary

I and O propositions are subcontrary.

It is always between Particulars. 

It is the opposite of the Contrary. 

Both Statements can't be False at the same time but both can be True. 

If One is False the other will be true definitely. 

If One is True the other will be Doubtful

For Example, Some women are writers Is True then, Some women are not writers is Doubtful. 
Subalternation

A and I, E and O propositions are Subalternation. ​

Between Universal and Particulars.

If Universal is True Particular will be False definitely. 

If Universal is False Particular will be True Doubtful. 

If Particular is False Universal will be False definitely. 

If Particular is True Universal will be Doubtful.  

Thus, "No women are writers" is false, and "Some women are not writers" is undetermined are correct. 

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