Any integer is rational. For instance, the integer 7 can be written as 7/1 which is a ratio or fraction of integers. Or we could say 14/2 or 21/3 if you wanted to get a bit creative. Since any integer is rational, this means it cannot be irrational. A real number is either rational or irrational. It cannot be both. The name "irrational" literally means "not rational". This is why statement 1 is false.
The claim "no whole numbers are irrational numbers" is a true statement because any whole number is rational (for very similar reasoning as explained in statement 1 above), which means it's not possible for a whole number to be irrational.
A rational number like 2/3 is not an integer. A quick way to check is to note that 2/3 = 0.67 approximately. Whole numbers and integers do not have any decimal portion to them. We have confirmed statement 3 is true.
The set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...} while the whole numbers is the set {0, 1, 2, 3, ...}. The key difference is that integers involve negative values. Whole numbers do not have negative values. Something like -7 is an integer, but it is not part of the set of whole numbers. Statement 4 is true because of this.
