Read the following statements and evaluate the conclusions based on traditional syllogistic logic. Consider the statements to be absolutely true, even if they appear contrary to known facts. Determine which conclusion(s) logically follow from the given statements. Statements: All metals are elements. Some elements are gases. Conclusions: I. Some metals are gases. II. All gases being elements is a possibility.

Correct — A.
Rule: a definite conclusion must hold in every diagram, a possibility in at least one.

I. Some metals are gases: the gases among the elements can lie wholly outside the metals, so I is not forced.

II. No statement puts any gas outside the elements, so all gases being elements is allowed → II follows.

Only II follows → option (a).

Why the others are wrong

• (b)
  Both I and II follow — Both fails on I. "Some elements are gases" can be met by elements that are not metals, so no metal need be a gas.
• (c)
  Only Conclusion I follows — Only I has it backwards. I is not forced, since the gaseous elements may all be non-metals, while II is a possibility no statement rules out.
• (d)
  Neither I nor II follows — Neither rejects II, but a possibility only has to fit the statements. Nothing places any gas outside the elements, so all gases being elements is allowed.

Syllogism conclusions come in two kinds. A definite conclusion ("Some metals are gases") must be true in every diagram the statements allow. A possibility must be true in at least one.

Draw metals inside elements. Gases overlap elements, but that overlap can miss the metal circle entirely, so I fails.

Nothing pushes gases outside elements, so the gas circle can sit wholly inside the element circle, and II holds.

Key facts

• "All A are B" with "Some B are C" gives no definite link between A and C.
• A possibility conclusion follows if at least one valid diagram makes it true.
• "Some elements are gases" does not rule out every gas being an element.

Common traps

• Chaining 'All metals are elements' and 'Some elements are gases' into 'Some metals are gases'
• Rejecting a possibility because it is not certain

No directly related past PYQ was found.