Proposition Pair Analysis: Contradictories

The question asks us to identify a pair of propositions that share a specific logical relationship: they can neither be true simultaneously, nor can they be false simultaneously. This relationship defines contradictory propositions. Contradictories must always have opposite truth values; if one is true, the other must be false, and vice versa.

Let's first classify the given propositions:

• A: All printers are computer peripherals.
  This is a Universal Affirmative statement.
• B: Some computer peripherals are printers.
  This is logically equivalent to "Some printers are computer peripherals", making it a Particular Affirmative statement.
• C: Some printers are not computer peripherals.
  This is a Particular Negative statement.
• D: No printers are computer peripherals.
  This is a Universal Negative statement.

Propositions A and C: Contradictory Pair

Now, let's examine the relationship between Proposition A and Proposition C:

• Proposition A asserts that the entire set of printers is contained within the set of computer peripherals.
• Proposition C asserts that there is at least one printer that falls outside the set of computer peripherals.

These two propositions, A and C, are contradictory.

Here's the reasoning:

• If Proposition A is true, it means every printer is indeed a computer peripheral. In this case, Proposition C (claiming some printers are *not* computer peripherals) must logically be false.
• Conversely, if Proposition A is false, it means the statement "All printers are computer peripherals" is not true. The direct consequence of this negation is that there must exist at least one printer which is not a computer peripheral. This is exactly what Proposition C states. Thus, if A is false, C must be true.

Because Propositions A and C necessarily have opposite truth values, they satisfy the condition of being neither true together nor false together.

Analysis of Other Proposition Pairs

Let's briefly look at why other combinations presented in the options do not fit the criteria:

• A and D (All printers are peripherals vs. No printers are peripherals): These are contraries. They cannot both be true, but they can both be false (e.g., if some printers are peripherals and some are not).
• B and C (Some printers are peripherals vs. Some printers are not peripherals): These are subcontraries. They cannot both be false, but they can both be true.
• A and B (All printers are peripherals vs. Some printers are peripherals): If A is true, B must also be true. They can be true together, so they are not contradictories.

Based on this logical analysis, the pair of propositions that are contradictory is A and C.