Math / Discrete

Question1) Let $X=\{x \in \mathbb{Z}:|x| \leq 3\}$ and $Y=\{-3,-2,-1,0,1,2,3\}$ . Then A) $X \subsetneq Y$ B) $X \neq Y$ C) $Y \subsetneq X$ D) $X=Y$ E) NOTA

Studdy Solution

STEP 1

1. $X$ is defined as the set of integers $x$ such that the absolute value of $x$ is less than or equal to 3.
2. $Y$ is explicitly given as the set $\{-3, -2, -1, 0, 1, 2, 3\}$ .
3. We need to determine the relationship between the sets $X$ and $Y$ .

STEP 2

1. Determine the elements of set $X$ .
2. Compare the elements of $X$ and $Y$ .
3. Determine the correct relationship between $X$ and $Y$ .

STEP 3

Determine the elements of set $X$ :
Given $X = \{ x \in \mathbb{Z} : |x| \leq 3 \}$ , this means $x$ can be any integer whose absolute value is less than or equal to 3.
Thus, $X = \{-3, -2, -1, 0, 1, 2, 3\}$ .

STEP 4

Compare the elements of $X$ and $Y$ :
We have $X = \{-3, -2, -1, 0, 1, 2, 3\}$ and $Y = \{-3, -2, -1, 0, 1, 2, 3\}$ .
Both sets contain the exact same elements.

STEP 5

Determine the correct relationship between $X$ and $Y$ :
Since $X$ and $Y$ contain the same elements, we conclude that $X = Y$ .
Therefore, the correct answer is:
D) $X = Y$
The correct relationship is $\boxed{D}$ .

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