In each of the following questions two statements are given. Which are…
2023
In each of the following questions two statements are given. Which are followed by four conclusions (1), (2), (3) and (4). Choose the conclusions which logically follow from the given statements. Statements: All the phones are scales. All the scales are calculators.Conclusions:1. All the calculators are scales.2. All the phones are calculators3. All the scales are phones.4. Some calculators are phones.
- A.
Only (1) and (4)
- B.
Only (3) and (4)
- C.
Only (2) and (4)
- D.
Only (1) and (2)
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Correct answer: C
Answer: Only the statements "All the phones are calculators" and "Some calculators are phones" follow.
Given statements:
All the phones are scales.
All the scales are calculators.
Conclusions that follow:
All the phones are calculators: This follows by transitivity because phones are a subset of scales and scales are a subset of calculators, so phones are a subset of calculators.
Some calculators are phones: Since every phone is a calculator, those phones (if any exist) are calculators; therefore there are calculators that are phones.
Conclusions that do not follow:
All the calculators are scales: This is the converse of a given statement. The given statements say scales are calculators, not that calculators are scales, so this does not follow.
All the scales are phones: This is also the converse of a given statement. The given statements say phones are scales, not that scales are phones, so this does not follow.