A student listed the following properties of Rational Numbers. Which one/ones…

A number is called a rational number when it can be written in the form p/q, where p and q are integers and q is not equal to 0. This single definition covers every integer (since any integer n equals n/1), every fraction (a ratio of one integer to another), and zero itself (since 0 equals 0/1).

1. Statement (a): Any integer n can be written as n/1, which already has the form p/q with q = 1, an integer not equal to 0. So every integer is a rational number, and statement (a) is true.

2. Statement (b): Zero can be written as 0/1, which also has the form p/q with p = 0 and q = 1. So zero meets the definition of a rational number, and the claim that zero is not a rational number is false.

3. Statement (c): A fraction is, by definition, one integer written over another integer -- exactly the p/q form required. So every fraction is a rational number, and statement (c) is true.

Testing this against concrete examples confirms it: -5 (an integer) equals -5/1, 3/4 (a fraction) is already in ratio form, and 0 equals 0/1 -- all three fit the rational-number test, and only the claim that zero is excluded fails it. So the properties that hold together are (a) and (c).