First let's define the sets that we will be using:
Integers: Are these numbers that can be written as an addition or subtraction of ones.
Rational numbers: Are these numbers that can be written as the quotient of two integers.
Irrational numbers: Are these numbers that can't be written as the quotient of two integers.
With this, we will see that the true options are A and D.
Now, to see which statements are true and which ones are false, let's analyze each one of them:
<em>a) All integers are rational.</em>
True, each integer number N can be written as:
N = N/1
Thus an integer number is a rational number.
<em>b) if a number is rational, then it must be a whole number.</em>
False, 1/2 = 0.5 is a rational number and is not a whole number.
<em>c) Some irrational numbers are intergers</em>
False, as we already see, all integers are rational numbers.
<em>d) all irrational numbers are real numbers</em>
True, we define real numbers as the union of the set of the irrational numbers and rational numbers, thus an irrational number is a real number.
e) No whole numbers are integers.
False, all whole numbers are integers <u>(but not all integers are whole numbers).</u>
So the ones that are true are: a and d.
If you want to learn more, you can read:
brainly.com/question/24540629