A set X is said to be closed under an operation OP if, for any elements in X, applying OP to them gives an element in X. For example, the set of integers is closed under multiplication because if we take any two integers, their product is also an integer.

Question 3. (10 points) A set X is said to be closed under an operation OP if, for any elements in X applying OP to them gives an element in X. For example, the set of integers is closed under multiplication because if we take any two integers, their product is also an integer. For each of the sentences below, (1) first determine if it is a closure claim, then (2) determine if the sentence is true or false For example, for the sentence "The product of any two prime numbers is not prime" is (1) not a closure claim but (2) is true. a. Concatenating two strings over the alphabet ? gives a string over the alphabet ?. b. The reversal of a string over the alphabet ? is a string over the alphabet ?. c. The intersection of two infinite sets of integers is an infinite set of integers. d. The union of two countably infinite sets of real numbers is an uncountable set of real numbers. e. The power set of a finite set of positive numbers is a finite set of positive numbers