First slide

Introduction to sets

Question

$If X = \{8^{n} - 7 n - 1, n \in N\} and y = {49 n - 49, n \in N} t h e n$

Easy

A

$X \subset Y$
B

$Y \subset X$
C

$X = Y$
D

$X \cap Y = ϕ$

Solution

$\begin{matrix} X = \{8^{n} - 7 n - 1, n \in N\} \\ = {0, 49, 490, \dots} \\ Y = {49 n - 49, n \in N} \\ = {0, 49, 98, 147, \dots} \end{matrix}$
Clearly, every element of X is in Y but every element of Y is not in X.
$∴ X \subset Y$

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