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Abeger · Answer 1 · 2024-03-07T22:24:36+0000

Part A:

$B\cap D$ is asking for what the sets B and D have in common:

$B\cap D = \{4\}$

since B and D only have 4 in common.

Now
$(B \cap D)'$ is asking for all of the things in the universal set
that are not in
$B\cap D$ . That's what the little tick mark on the right side means.

$(B \cap D)' = \{2, 3, 6, 7\}$

Part B:

$B' = \{2, 3, 7\}$ since those are the things not in B.

$D=\{3, 4\}$

$B'\cup D$ is asking for all the things in either
or
.

$B'\cup D = \{2, 3, 4, 7\}$

(We don't need to list 3 twice, even though it was in both sets. )

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