Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$.

Question

After working it out on a number line, I got: $\{4, 5, 6\}$.

As it stands, the expression contains the integers that do not belong to the set $B$ that cross into $C$. This would result in $4, 5, 6$. Number $7$ would not be included because of the soft brackets surrounding $C = (2, 7)$. Is this correct?

Indeed, $A \cap (B^c \cap C)=\mathbb{Z} \cap (\pi, 7)={4,5,6}$ — Alonso Delfín, Aug 14 '15 at 00:45
@AlonsoDelfín I agree with your final answer, but $B^c\cap C \neq {4,5,6}$. It equals the interval $(\pi, 7)$. — coldnumber, Aug 14 '15 at 00:47

score 1 · Accepted Answer · answered Aug 14 '15 at 00:46

1

You're right.

Here are the intermediate steps: $B^c=(-\infty, -1) \cup (\pi, \infty)$, so $B^c\cap C = (\pi, 7)$.

And as you wrote, the only integers in that interval are $4,5,6$.

answered Aug 14 '15 at 00:46

coldnumber

3,721

score 0 · Answer 2 · answered Aug 14 '15 at 00:48

0

You are correct.

$B^\mathsf{c} \cap C = (\pi, 7)$

$A \cap (B^\mathsf{c} \cap C) = \mathbb{Z} \cap (\pi, 7) = \{4,5,6\}$

answered Aug 14 '15 at 00:48

727

1,607

score 0 · Answer 3 · answered Aug 14 '15 at 01:55

You're looking for all numbers

in $\mathbb Z$; and
in $(-\infty,-1)\cup(\pi,\infty)$; and
in $(2,7)$.

In words, what you're looking for are

all integers;
that are either less than $-1$ or greater than $\pi$; and
that are strictly between $2$ and $7$.

These numbers are $\{4,5,6\}$.

Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$.

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