The following provided statements are given with its truth-value in parentheses,

Question

The following provided statements are given with its truth-value in parentheses, do the listed operation to be performed on that statement. Supply the new statement and the truth-value of the new statement.

Given Statement                     Operation                  New Statement                            Truth-value

1. All non-A are B (T)           contraposition            _______________________             ______

2. No A are non-B (F)                   obversion              _______________________             ______

3. No A are B (F)                   contradiction             _______________________             ______

4. No A are non-B (F)                 conversion              _______________________             ______

5. Some non-A are not non-B (F) contraposition      _______________________             ______

6. All A are non-B (T)                  obversion.             _______________________             ______

7. All A are B (T)                   contradiction             _______________________             ______

8. Some non-A are not B (T)         obversion.            _______________________             ______

9. All B are A (T)                         conversion             _______________________              ______

10. Some A are non-B (F)     contraposition             _______________________              ______

11. All non-A are non-B (T)   contradiction             _______________________              ______

12. Some non-B are non-A (F)     conversion             _______________________              ______

Explanation / Answer

If something is not B then it is A (T) as the conclusion and premise position changes in contrapositioning and the not is added also it is true as the forst one was true and the meaning hasnt changed All A are non B (T) as the obversion includes changing the affirmative to negative and vice versa and its true as the logic is reversed all B are A (T) as two contradictory statements are used as the logic is reverse No B are non A (F)as the subject is change and the logic remains the same In some cases if something is not B them it is also not A (F) as the conclusion and premise position changes in contrapositioning and the not is added also it is false as the first one was true and the meaning hasnt changed All A are B (F) the obversion includes changing the affirmative to negative and vice versa and its false as the logic is reversed no B is A (T) as statement is contradicted and the logic is contradicted Some non A are B (T) as negative is changed to affirmative and as per the statement which is true some non A are not B then some will be B also All A are B (T) as the subject is change and the logic remains the same Non B are A in some cases (F) as the conclusion and premise position changes in contrapositioning and the not is added also it is false as the first one was false and the meaning hasnt changed All are non B are not non A (F) as statement is contradicted and the logic is contradicted Some non A are non B as the subject is change and the logic remains the same

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