Which of the following statements can neither be both true, nor can they both be together false?

A. All bread is nutritious.

B. Some bread is nutritious.

C. Some bread is not nutritious.

D. No bread is nutritious.

Choose the correct answer from the options given below:

The correct answer is 
Important PointsThe correct answer is A and C Only.

Statement A: "All bread is nutritious" - This statement asserts that every instance of bread is nutritious.

• For the statements to be true, every single piece of bread must be nutritious. If even one instance of bread is not nutritious, the statement would be false.
• Therefore, statement A cannot be both true and false together.

Statement C: "Some bread is not nutritious" -

This statement acknowledges that there exists at least one instance of bread that is not nutritious. If even one piece of bread is nutritious, then this statement would be false. Therefore, statement C cannot be both true and false together.
Additional InformationStatement B: "Some bread is nutritious" -

• This statement acknowledges that there exists at least one instance of bread that is nutritious.
• This statement can be true even if some bread is not nutritious. Therefore, it is possible for statement B to be true and false at the same time.

Statement D: "No bread is nutritious" -

• This statement asserts that there is no instance of bread that is nutritious.
• For the statements to be true, not a single piece of bread must be nutritious. If even one instance of bread is nutritious, the statement would be false. Therefore, statement D cannot be both true and false together.

In summary, statements A and C cannot be both true and false together, while statements B and D can have the possibility of being both true and false together.