The number $t$ is irrational. Which statement about $t - \pi$ is true? $\newline$ Choices: $\newline$ (A) $t - \pi$ is rational. $\newline$ (B) $t - \pi$ is irrational. $\newline$ (C) $t - \pi$ can be rational or irrational, depending on the value of $t$ .

Full solution

Q. The number

t

is irrational. Which statement about

t - \pi

is true?

\newline

Choices:

\newline

(A)

t - \pi

is rational.

\newline

(B)

t - \pi

is irrational.

\newline

(C)

t - \pi

can be rational or irrational, depending on the value of

t

Identify Type of $\pi$ : Identify whether $\pi$ is a rational or irrational number. $\newline$ $\pi$ is a well-known mathematical constant that represents the ratio of a circle's circumference to its diameter. $\pi$ is an irrational number.
Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be either rational or irrational. It depends on the specific values of the numbers involved.
Outcomes for $t - \pi$ : Analyze the possible outcomes for $t - \pi$ . If $t$ is an irrational number that is not related to $\pi$ in a simple way (for example, $t$ is not equal to $\pi$ or $-\pi$ ), then $t - \pi$ will also be irrational. However, if $t$ is some irrational number that when subtracted by $\pi$ results in a rational number (for example, if $t - \pi$ $0$ , where $t - \pi$ $1$ is rational), then $t - \pi$ would be rational.
Correct Statement: Determine the correct statement based on the analysis. $\newline$ Since there are scenarios where $t - \pi$ can be rational and others where it can be irrational, depending on the specific value of $t$ , the correct statement is that $t - \pi$ can be rational or irrational, depending on the value of $t$ .