Identifying Contradictory Ducks & Birds Statements

This question asks us to find which pair of statements about ducks and birds contradict each other. Two statements contradict each other if they cannot both be true at the same time, and they also cannot both be false at the same time. Essentially, one statement must be true while the other is false.

Analyzing the Statements

Let's break down each statement:

• Statement A: All ducks are birds. (This is a universal statement, saying every single duck belongs to the category 'birds'.)
• Statement B: Some ducks are birds. (This is a particular statement, saying at least one duck exists, and that duck is a bird.)
• Statement C: Some ducks are not birds. (This is a particular statement, saying at least one duck exists, and that duck is not a bird.)
• Statement D: No ducks are birds. (This is a universal statement, saying zero ducks belong to the category 'birds'.)

Contradictory Pairs Explained

In logic, certain pairs of statements are always opposites (contradictories). The main contradictory pairs are:

• "All S are P" contradicts "Some S are not P".
• "No S are P" contradicts "Some S are P".

Let's apply this to our statements where 'S' is 'ducks' and 'P' is 'birds':

• Statement A ("All ducks are birds") contradicts Statement C ("Some ducks are not birds").
• Statement D ("No ducks are birds") contradicts Statement B ("Some ducks are birds").

Evaluating the Given Options

Now let's check the options provided in the question against our understanding:

• Option 1: A and D Only - Statement A ("All ducks are birds") and Statement D ("No ducks are birds") are *contraries*. They cannot both be true, but they could potentially both be false (e.g., if some ducks are birds, and some ducks are not birds). They don't contradict each other completely.
• Option 2: B and C Only - Statement B ("Some ducks are birds") and Statement C ("Some ducks are not birds") are *subcontraries*. They cannot both be false, but they can both be true. For example, if ducks exist, it's possible that some are birds and others are not.
• Option 3: B and D Only - Statement B ("Some ducks are birds") and Statement D ("No ducks are birds") are indeed contradictories. If it's true that "Some ducks are birds", then it must be false that "No ducks are birds". Conversely, if it's true that "No ducks are birds", it must be false that "Some ducks are birds".
• Option 4: C and D Only - Statement C ("Some ducks are not birds") and Statement D ("No ducks are birds"). If "No ducks are birds" (D) is true, then "Some ducks are not birds" (C) is also necessarily true (assuming ducks exist). Therefore, they cannot both be false, but they are not contradictories because they can both be true. Statement D implies Statement C if the subject class ('ducks') is not empty.

Conclusion

Based on the analysis, the statements that contradict each other are B ("Some ducks are birds") and D ("No ducks are birds").