Question

(b) true or false?
statement\ttrue\tfalse
some irrational numbers are whole numbers.\t○\t○
all whole numbers are rational numbers.\t○\t○
no integers are irrational numbers.\t○\t○
all integers are rational numbers.\t○\t○

Explanation:

Step1: Analyze "Some irrational numbers are whole numbers"

Irrational numbers are non - repeating, non - terminating decimals. Whole numbers are 0, 1, 2, 3, … Whole numbers can be written as a fraction with denominator 1 (e.g., \(2=\frac{2}{1}\)), so they are rational. So irrational numbers and whole numbers have no overlap. So this statement is False.

Step2: Analyze "All whole numbers are rational numbers"

A rational number is a number that can be written as \(\frac{a}{b}\) where \(a,b\) are integers and \(b
eq0\). Whole numbers \(n\) can be written as \(\frac{n}{1}\), so all whole numbers are rational. This statement is True.

Step3: Analyze "No integers are irrational numbers"

Integers can be written as \(\frac{n}{1}\) (where \(n\) is an integer), so they are rational. Irrational numbers are not rational, so no integers are irrational. This statement is True.

Step4: Analyze "All integers are rational numbers"

An integer \(n\) can be expressed as \(\frac{n}{1}\), which fits the definition of a rational number (\(a = n\), \(b = 1\), \(b
eq0\)). So all integers are rational. This statement is True.

Answer:

• "Some irrational numbers are whole numbers": False
• "All whole numbers are rational numbers": True
• "No integers are irrational numbers": True
• "All integers are rational numbers": True