Question

checkup
for questions 1 and 2, state whether each statement is true or false. explain your answer. use the
venn diagram.
venn diagram: real numbers (universal set), with rational numbers (circle) containing integers (circle), containing whole numbers (circle), containing natural numbers (circle); and irrational numbers (separate circle) within real numbers

1. all real numbers are irrational numbers.
2. some numbers are both rational and irrational.

Explanation:

Question 1:

Step1: Recall real number definition

Real numbers include rational (e.g., integers, fractions) and irrational (e.g., $\sqrt{2}$) numbers.

Step2: Analyze the statement

The statement says "All real numbers are irrational". But real numbers have rational numbers too (like $2$, $\frac{1}{2}$), so the statement is false.

Step1: Recall rational/irrational definitions

Rational numbers can be expressed as $\frac{p}{q}$ ($p,q$ integers, $q
eq0$); irrational cannot.

Step2: Analyze the statement

A number can't be both (their sets are disjoint, as seen in the Venn diagram: rational and irrational circles don't overlap). So the statement is false.

Answer:

False. Because real numbers consist of both rational and irrational numbers, not all real numbers are irrational (e.g., integers like 3 are rational and real).

Question 2: