GATE 2026 MA – Question 62

Topology · Topological Spaces and Constructions · 2 marks · Numerical answer

X={5,6,7,8,9,10} has topology {∅,X,{5,6,7},{8,9,10}}. How many subsets are neither open nor closed? (integer)

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Correct answer: 60 to 60

Explanation

There are 2⁶=64 subsets. All four listed opens are also closed because their complements are among the same four sets. There are no other closed sets. Remove these four from all subsets: **60**.

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