Math / Discrete

QuestionLet the Universal set be the letters a through $j: U=\{a, b, \ldots, i, j\}$ . Let $A=\{c, d, i, j\}, B=\{c, d, e, h\}$ , and $C=\{a, d, h, j\}$ List the elements of the set $(A \cap B) \cup C$ $\square$

Studdy Solution

STEP 1

What is this asking? Find the elements that are in both A and B, and then combine those elements with the elements in C. Watch out! Don't mix up union and intersection!
Intersection means what they have in common, and union means everything together.

STEP 2

1. Find the Intersection
2. Find the Union

STEP 3

Let's find the intersection of A and B!
Remember, the intersection $A \cap B$ includes only the elements that are present in both sets A and B.

STEP 4

Looking at our sets, $A = \{c, d, i, j\}$ and $B = \{c, d, e, h\}$ , we see that both sets contain the elements c and d.
So, $A \cap B = \{c, d\}$ .
Awesome!

STEP 5

Now, we need to find the union of $(A \cap B)$ and C.
Remember, the union of two sets includes all the elements from both sets, without repeating any element.

STEP 6

We already know that $A \cap B = \{c, d\}$ and we're given that $C = \{a, d, h, j\}$ .

STEP 7

So, when we combine these sets, we get $(A \cap B) \cup C = \{c, d\} \cup \{a, d, h, j\} = \{a, c, d, h, j\}$ .
Notice how we only included d once, even though it appears in both sets!

STEP 8

The elements of the set $(A \cap B) \cup C$ are $\{a, c, d, h, j\}$ .

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QuestionLet the Universal set be the letters a through $j: U=\{a, b, \ldots, i, j\}$ . Let $A=\{c, d, i, j\}, B=\{c, d, e, h\}$ , and $C=\{a, d, h, j\}$ List the elements of the set $(A \cap B) \cup C$ $\square$

Studdy Solution

STEP 1

What is this asking? Find the elements that are in both A and B, and then combine those elements with the elements in C. Watch out! Don't mix up union and intersection!
Intersection means what they have in common, and union means everything together.

STEP 2

1. Find the Intersection
2. Find the Union

STEP 3

Let's find the intersection of A and B!
Remember, the intersection $A \cap B$ includes only the elements that are present in both sets A and B.

STEP 4

Looking at our sets, $A = \{c, d, i, j\}$ and $B = \{c, d, e, h\}$ , we see that both sets contain the elements c and d.
So, $A \cap B = \{c, d\}$ .
Awesome!

STEP 5

Now, we need to find the union of $(A \cap B)$ and C.
Remember, the union of two sets includes all the elements from both sets, without repeating any element.

STEP 6

We already know that $A \cap B = \{c, d\}$ and we're given that $C = \{a, d, h, j\}$ .

STEP 7

So, when we combine these sets, we get $(A \cap B) \cup C = \{c, d\} \cup \{a, d, h, j\} = \{a, c, d, h, j\}$ .
Notice how we only included d once, even though it appears in both sets!

STEP 8

The elements of the set $(A \cap B) \cup C$ are $\{a, c, d, h, j\}$ .

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Studdy Solution

STEP 1

What is this asking? Find the elements that are in both *A* and *B*, and then combine those elements with the elements in *C*. Watch out! Don't mix up union and intersection!Intersection means what they have *in common*, and union means *everything together*.

STEP 2

1. Find the Intersection2. Find the Union

STEP 3

Let's **find** the intersection of *A* and *B*!Remember, the intersection A∩BA \cap BA∩B includes only the elements that are present in *both* sets *A* and *B*.

STEP 4

Looking at our sets, A={c,d,i,j}A = \{c, d, i, j\}A={c,d,i,j} and B={c,d,e,h}B = \{c, d, e, h\}B={c,d,e,h}, we see that both sets contain the elements *c* and *d*.So, A∩B={c,d}A \cap B = \{c, d\}A∩B={c,d}.Awesome!

STEP 5

Now, we need to find the union of (A∩B)(A \cap B)(A∩B) and *C*.Remember, the union of two sets includes *all* the elements from both sets, without repeating any element.

STEP 6

We already know that A∩B={c,d}A \cap B = \{c, d\}A∩B={c,d} and we're given that C={a,d,h,j}C = \{a, d, h, j\}C={a,d,h,j}.

STEP 7

So, when we combine these sets, we get (A∩B)∪C={c,d}∪{a,d,h,j}={a,c,d,h,j}(A \cap B) \cup C = \{c, d\} \cup \{a, d, h, j\} = \{a, c, d, h, j\}(A∩B)∪C={c,d}∪{a,d,h,j}={a,c,d,h,j}.Notice how we only included *d* once, even though it appears in both sets!

STEP 8

The elements of the set (A∩B)∪C(A \cap B) \cup C(A∩B)∪C are {a,c,d,h,j}\{a, c, d, h, j\}{a,c,d,h,j}.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Find the elements that are in both A and B, and then combine those elements with the elements in C. Watch out! Don't mix up union and intersection!
Intersection means what they have in common, and union means everything together.

1. Find the Intersection
2. Find the Union

Let's find the intersection of A and B!
Remember, the intersection $A \cap B$ includes only the elements that are present in both sets A and B.

Looking at our sets, $A = \{c, d, i, j\}$ and $B = \{c, d, e, h\}$ , we see that both sets contain the elements c and d.
So, $A \cap B = \{c, d\}$ .
Awesome!

Now, we need to find the union of $(A \cap B)$ and C.
Remember, the union of two sets includes all the elements from both sets, without repeating any element.

We already know that $A \cap B = \{c, d\}$ and we're given that $C = \{a, d, h, j\}$ .

So, when we combine these sets, we get $(A \cap B) \cup C = \{c, d\} \cup \{a, d, h, j\} = \{a, c, d, h, j\}$ .
Notice how we only included d once, even though it appears in both sets!

The elements of the set $(A \cap B) \cup C$ are $\{a, c, d, h, j\}$ .