Questions: Let X and Y be the following sets: X=15,12 Y=12,15,2 Which of the following is the set X Y ? Choose 1 answer: (A) 2,12,15 (B) (C) 2 (D) 12,15

Transcript text: Let $X$ and $Y$ be the following sets: \[ \begin{array}{l} X=\{15,12\} \\ Y=\{12,15,2\} \end{array} \] Which of the following is the set $X \backslash Y$ ? Choose 1 answer: (A) $\{2,12,15\}$ (B) $\}$ (C) $\{2\}$ (D) $\{12,15\}$

Solution

Solution Steps

Step 1: Identify the sets $ X $ and $ Y $

Given: \[ X = \{15, 12\} \] \[ Y = \{12, 15, 2\} \]

Step 2: Understand the operation $ X \backslash Y $

The operation $ X \backslash Y $ represents the set difference, which includes all elements that are in $ X $ but not in $ Y $.

Step 3: Compute $ X \backslash Y $

Compare the elements of $ X $ with those of $ Y $:

The element $ 15 $ is in both $ X $ and $ Y $, so it is not included in $ X \backslash Y $.
The element $ 12 $ is in both $ X $ and $ Y $, so it is not included in $ X \backslash Y $.

Since there are no elements in $ X $ that are not in $ Y $, the set $ X \backslash Y $ is empty.