Let $X = \{ x \mid x 7 \}$ and $Y = \{ x \mid x \leq - 8 \}$. Determine the given union. Express the answer in interval notal $X \cup Y$
A) $( - \infty , - 8 ] \cup ( 7 , \infty )$
B) $[ - 8,7 )$
C) $( - 8,7 ]$
D){ } .

Question

Let $X = \{ x \mid x > 7 \}$ and $Y = \{ x \mid x \leq - 8 \}$. Determine the given union. Express the answer in interval notal $X \cup Y$
A) $( - \infty , - 8 ] \cup ( 7 , \infty )$
B) $[ - 8,7 )$
C) $( - 8,7 ]$
D){  } .

Quizplus · Accepted Answer

The set $X$ includes all numbers greater than 7, and $Y$ includes all numbers less than or equal to -8. The union of these two sets, $X \cup Y$, combines both conditions, resulting in two separate intervals: all numbers less than or equal to -8 and all numbers greater than 7. This is correctly represented by the interval notation $( - \infty , - 8 ] \cup ( 7 , \infty )$.

Let X={x∣x>7}X = \{ x \mid x > 7 \}X={x∣x>7} And Y={x∣x≤−8}Y = \{ x \mid x \leq - 8 \}Y={x∣x≤−8}

Let $X = \{ x \mid x > 7 \}$ And $Y = \{ x \mid x \leq - 8 \}$