Which of the following statements is logically equivalent to the statement -' No metals are gases'?

Question

Question

This question was previously asked in

UGC NET Paper 1: Held on 24th Feb 2023 Shift 2

Answer 1

The statement "No metals are gases" can be rewritten in a logical form as "For all x, if x is a metal, then x is not a gas."

Key Points

"No gases are metals," has the same form as the original statement, but with the subject and predicate reversed.
This is a logically equivalent statement to the original statement, as it is also saying that there is no overlap between the set of metals and the set of gases.

Additional Information

Option 1, "All non-metals are gases," is not logically equivalent to the original statement, as it is a statement about all non-metals, not just the relationship between metals and gases.
Option 3, "No metals are non-gases," is also not logically equivalent to the original statement, as it allows for the possibility that metals may be gases.
Option 4, "All non-gases are non-metals," is not logically equivalent to the original statement, as it is a statement about all non-gases, not just the relationship between metals and gases.

Therefore, "No gases are metals," is the logically equivalent statement to the original statement "No metals are gases."