Question

What are the elements of the set S={x∈(-100,-50)┤| x≡6 mod 17}?

Answer 1

Answer on Question #71821 – Math – Discrete Mathematics

Question

What are the elements of the set $S = \{x \in (-100, -50) \mid |x \equiv 6 \mod 17\}$?

Solution

From $x \equiv 6 \mod 17$ we can write $x$ as $x = 17t + 6$, where $t$ is integer number. According to the condition of problem $x \in (-100, -50)$. Hence, we obtain the inequality

$$\begin{array}{l} -100 < 17t + 6 < -50 \rightarrow -106 < 17t < -56 \rightarrow -\frac{106}{17} < t < -\frac{56}{17} \\ -6\frac{4}{17} < t < -3\frac{5}{17}. \end{array}$$

Because $t$ is an integer, the solution of inequality $t = \{-6, -5, -4\}$. Therefore $x$ of the set $S$

$$\begin{array}{l} t = -6 \rightarrow x = -6 \cdot 17 + 6 = -96 \\ t = -5 \rightarrow x = -5 \cdot 17 + 6 = -79 \\ t = -4 \rightarrow x = -4 \cdot 17 + 6 = -62 \\ S = \{-96, -79, -62\} \end{array}$$

To implement the search on the computer, you must specify a cycle from -100 to -50 in steps of 1 and check the condition for each element $x - 6$ must be divisible by 17. Get the same answer.

Answer: $S = \{-96, -79, -62\}$.

Answer provided by https://www.AssignmentExpert.com