Math / Discrete

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

Studdy Solution

STEP 1

What is this asking? We need to find the letters that are both in set A AND in the combined set of B OR C. Watch out! Don't mix up intersection and union!
Intersection means "AND" (elements in BOTH sets), while union means "OR" (elements in EITHER set).

STEP 2

1. Find the union of B and C.
2. Find the intersection of A and the result from the previous step.

STEP 3

Let's start by finding $B \cup C$ , which means all the elements in B OR C (or both!). B has $\{a, c, e, g\}$ and C has $\{a, b, d, e\}$ .
Combining these, we get $\{a, b, c, d, e, g\}$ .
Notice how we only include a and e once, even though they appear in both sets!

STEP 4

Now, we want to find $A \cap (B \cup C)$ .
This means we're looking for the letters that are in BOTH A AND the set we just found, $\{a, b, c, d, e, g\}$ .

STEP 5

Set A is $\{a, c, d, h\}$ .
Let's compare it to $\{a, b, c, d, e, g\}$ .
Both sets contain $\{a, c, d\}$ , so that's our intersection!

STEP 6

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

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

Studdy Solution

STEP 1

What is this asking? We need to find the letters that are both in set A AND in the combined set of B OR C. Watch out! Don't mix up intersection and union!
Intersection means "AND" (elements in BOTH sets), while union means "OR" (elements in EITHER set).

STEP 2

1. Find the union of B and C.
2. Find the intersection of A and the result from the previous step.

STEP 3

Let's start by finding $B \cup C$ , which means all the elements in B OR C (or both!). B has $\{a, c, e, g\}$ and C has $\{a, b, d, e\}$ .
Combining these, we get $\{a, b, c, d, e, g\}$ .
Notice how we only include a and e once, even though they appear in both sets!

STEP 4

Now, we want to find $A \cap (B \cup C)$ .
This means we're looking for the letters that are in BOTH A AND the set we just found, $\{a, b, c, d, e, g\}$ .

STEP 5

Set A is $\{a, c, d, h\}$ .
Let's compare it to $\{a, b, c, d, e, g\}$ .
Both sets contain $\{a, c, d\}$ , so that's our intersection!

STEP 6

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

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Studdy Solution

STEP 1

What is this asking? We need to find the letters that are both in set *A* AND in the combined set of *B* OR *C*. Watch out! Don't mix up intersection and union!Intersection means "AND" (elements in BOTH sets), while union means "OR" (elements in EITHER set).

STEP 2

1. Find the union of *B* and *C*.2. Find the intersection of *A* and the result from the previous step.

STEP 3

STEP 4

Now, we want to find A∩(B∪C)A \cap (B \cup C)A∩(B∪C).This means we're looking for the letters that are in BOTH *A* AND the set we just found, {a,b,c,d,e,g}\{a, b, c, d, e, g\}{a,b,c,d,e,g}.

STEP 5

Set *A* is {a,c,d,h}\{a, c, d, h\}{a,c,d,h}.Let's compare it to {a,b,c,d,e,g}\{a, b, c, d, e, g\}{a,b,c,d,e,g}.Both sets contain {a,c,d}\{a, c, d\}{a,c,d}, so that's our **intersection**!

STEP 6

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

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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? We need to find the letters that are both in set A AND in the combined set of B OR C. Watch out! Don't mix up intersection and union!
Intersection means "AND" (elements in BOTH sets), while union means "OR" (elements in EITHER set).

1. Find the union of B and C.
2. Find the intersection of A and the result from the previous step.

Now, we want to find $A \cap (B \cup C)$ .
This means we're looking for the letters that are in BOTH A AND the set we just found, $\{a, b, c, d, e, g\}$ .

Set A is $\{a, c, d, h\}$ .
Let's compare it to $\{a, b, c, d, e, g\}$ .
Both sets contain $\{a, c, d\}$ , so that's our intersection!

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