GATE 1990
January 30, 2024Question 7839 – GATE 2018
January 31, 2024Question 6671 – Closure-Property
Given the following statements :
(A) A class of languages that is closed under union and complementation has to be closed under intersection.
(B) A class of languages that is closed under union and intersection has to be closed under complementation.
Which of the following options is correct?
Correct Answer: C
Question 8 Explanation:
be closed under intersection but if a language is not closing under either of union or complementation then it can or can not be closed under intersection.
So here, Statement (A) is true because regular language, context sensitive language and recursive language are closed under union and complementation and they are also closing under intersection but recursive enumerable language is closed under union but not under complementation but still it is closed under intersection.
Statement (B): The meaning of given statement is that if a class of languages that is closed under union and intersection then it has to be closed under complementation but if a language is not closing under either of union or intersection then it can or can not be closed under complementation.
So here, Statement (B) is false because regular language, context sensitive language, recursive language and recursively enumerable language are closed under union and intersection but only regular language, context sensitive language and recursive language are closed under complementation , recursively enumerable language is not closing under complementation after being closed under union and intersection.
Hence statement (B) is not true.
So here, Statement (A) is true because regular language, context sensitive language and recursive language are closed under union and complementation and they are also closing under intersection but recursive enumerable language is closed under union but not under complementation but still it is closed under intersection.
Statement (B): The meaning of given statement is that if a class of languages that is closed under union and intersection then it has to be closed under complementation but if a language is not closing under either of union or intersection then it can or can not be closed under complementation.
So here, Statement (B) is false because regular language, context sensitive language, recursive language and recursively enumerable language are closed under union and intersection but only regular language, context sensitive language and recursive language are closed under complementation , recursively enumerable language is not closing under complementation after being closed under union and intersection.
Hence statement (B) is not true.
Both (A) and (B) are false.
Both (A) and (B) are true.
(A) is true, (B) is false.
(A) is false, (B) is true.