Question

Let the Universal set be the letters a through j: U = {a, b,

..., i, j}. Let A = {c, d, h, j}, B = {d, e, i, j}, and C = {c, e,
g, j} List the elements of the set A ∩ ( B ∪ C )

Answer 1

Answer: {c, d, j}

Work Shown

B ∪ C = B union C

B ∪ C = {d, e, i, j} union {c, e, g, j}

B ∪ C = {d, e, i, j, c, e, g, j}

B ∪ C = {d, e, i, j, c, g, j}

B ∪ C = {c, d, e, g, i, j}

A ∩ ( B ∪ C ) = A intersect ( B ∪ C )

A ∩ ( B ∪ C ) = {c, d, h, j} intersect {c, d, e, g, i, j}

A ∩ ( B ∪ C ) = {c, d, j}

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Explanation

B ∪ C is the union of set B and set C.

This is where we combine the two sets to form a single set. Toss any duplicates. It helps to sort the letters in alphabetical order.

The ∩ means intersection. We look at what set A and set (B ∪ C) have in common.

Side note: make sure not to confuse the universal set U with the union symbol ∪. Both look almost identical.

The Venn Diagram is shown below. The blue region is highlighted which visually represents A ∩ ( B ∪ C ).

Answer 2

First, we find the union of sets (B) and (C):

`(B \cup C = {c, d, e, g, i, j})`

Next, we find the intersection of set (A) with the result:

`(A \cap (B \cup C) = {c, d, j})`

Therefore, the elements of the set
`(A \cap (B \cup C)) are ({c, d, j).`

Explanation:

The set
`(A \cap (B \cup C))` consists of all elements that are in set (A) and also in the union of sets (B) and (C). To find the elements of this set, we first find the union of sets (B) and (C), and then find the intersection of set (A) with the result.

Given:

`(A = {c, d, h, j})`

`(B = {d, e, i, j})`

`(C = {c, e, g, j})`

First, we find the union of sets (B) and (C):

`(B \cup C = {c, d, e, g, i, j})`

Next, we find the intersection of set (A) with the result:

`(A \cap (B \cup C) = {c, d, j})`

Therefore, the elements of the set
`(A \cap (B \cup C)) are ({c, d, j).`