The Empty Set, many more. Step 3: Hence the set is infinite.

Correct answer: D. It is infinite

Explanation: There are irrational numbers strictly between 0 and 1; for example, √2/2 is approximately 0.707 and is irrational. Moreover, infinitely many distinct irrational numbers lie in this interval. For instance, the density of irrational numbers in the real numbers guarantees irrational numbers between any two different real numbers. Thus the set is infinite, and option D is correct.

Correct answer: C. It is infinite

Explanation: Taking n = 1, 2, 3, 4, and so on produces the distinct values 1, 1/2, 1/3, 1/4, and so on. Although these positive fractions become smaller and approach zero, they never become zero and the process of choosing a new natural number never ends. Thus the set has infinitely many elements, so option C is correct.

Correct answer: A. {5}

Explanation: Set A contains all numbers greater than 1 up to and including 5. Set B contains all numbers from 5, including 5, up to but not including 9. The only number common to both sets is 5. Hence their intersection is the singleton set {5}, not an interval extending on either side of 5.