Yes, the set of non-deterministic polynomial time (NP) problems is closed under the operation of union.
No, the set of nonregular languages is not closed under intersection.
Having a closed under composition set in abstract algebra is significant because it means that when two elements in the set are combined using the operation defined, the result will also be an element in the set. This property is important for ensuring that the set forms a mathematical structure that follows the rules of the operation consistently.
a set of instructions of how to turn on the computer would be considered an algorithm?
yes.
Yes, the set of non-deterministic polynomial time (NP) problems is closed under the operation of union.
No. 2/4 is not an even number.
They form a closed set under addition, subtraction or multiplication.
The set of even numbers is closed under addition, the set of odd numbers is not.
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
No, the set of nonregular languages is not closed under intersection.
Yes, the set is closed.
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
Yes. The empty set is closed under the two operations.
That is correct, the set is not closed.
Yes, the set of integers is closed under subtraction.
It is not closed under taking square (or other even) roots.