Question

1. which of the following is a rational number?

a. $\pi$
b. $\sqrt{2}$
c. $\frac{3}{5}$
d. $\sqrt{5}$

1. the additive identity element for real numbers is:

a. 0
b. 1
c. $-1$
d. $\infty$

1. what is the multiplicative inverse of 8?

a. 8
b. $\frac{1}{8}$
c. $-8$
d. 0

1. which property is illustrated by the equation $5 + 7 = 7 + 5$?

a. associative property
b. commutative property
c. distributive property
d. identity property

1. if $a = \\{1,2,3,4\\}$ and $b = \\{3,4,5,6\\}$, what is $a \cap b$?

a. $\\{1,2,3,4,5,6\\}$
b. $\\{3,4\\}$
c. $\\{1,2,5,6\\}$
d. $\emptyset$

1. the symbol $\subseteq$ means:

a. proper subset
b. subset
c. union
d. intersection

1. in a venn diagram, $a \cap b$ represents:

a. only in $a$
b. only in $b$
c. in both $a$ and $b$
d. outside both

1. which of the following is irrational?

Explanation:

Question 1

Step1: Recall rational number definition

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$.

Step2: Analyze each option

• Option A: $\pi$ is an irrational number (non - repeating, non - terminating decimal).
• Option B: $\sqrt{2}$ is irrational (cannot be expressed as a fraction of two integers).
• Option C: $\frac{3}{5}$ is in the form $\frac{p}{q}$ with $p = 3$, $q = 5$ (integers, $q

eq0$), so it is rational.

• Option D: $\sqrt{5}$ is irrational (cannot be expressed as a fraction of two integers).

Step1: Recall additive identity definition

The additive identity element of a set of numbers is an element which when added to any number in the set leaves the number unchanged.

Step2: Analyze each option

• Option A: For any real number $x$, $x + 0=x$. So 0 is the additive identity.
• Option B: $x + 1

eq x$ (unless $x = 0$), so 1 is not the additive identity.

• Option C: $x+( - 1)

eq x$ (unless $x = 1$), so - 1 is not the additive identity.

• Option D: $\infty$ is not a real number in the context of additive identity (and $x+\infty=\infty

eq x$ for finite $x$).

Step1: Recall multiplicative inverse definition

The multiplicative inverse of a non - zero number $a$ is a number $b$ such that $a\times b = 1$.

Step2: Find the multiplicative inverse of 8

Let the multiplicative inverse of 8 be $x$. Then $8\times x=1$. Solving for $x$, we get $x=\frac{1}{8}$.

• Option A: $8\times8 = 64

eq1$, so 8 is not the multiplicative inverse.

• Option B: $8\times\frac{1}{8}=1$, so $\frac{1}{8}$ is the multiplicative inverse.
• Option C: $8\times(-8)=-64

eq1$, so - 8 is not the multiplicative inverse.

• Option D: $8\times0 = 0

eq1$, so 0 is not the multiplicative inverse.

Answer:

C. $\frac{3}{5}$

Question 2