Math  /  Discrete

Question4. U={1,2,3,4,5,6,7,8,9,10},R={2,6,7,8},S={6,8,9}U=\{1,2,3,4,5,6,7,8,9,10\}, R=\{2,6,7,8\}, S=\{6,8,9\}, and T={3,4,5}T=\{3,4,5\}. Find RTR \cup T. A. {2,6,7,8,9}\{2,6,7,8,9\} B. {2,3,4,5,6,7,8}\{2,3,4,5,6,7,8\} C. \varnothing D. {1,9,10}\{1,9,10\}

Studdy Solution

STEP 1

What is this asking? We need to find all the unique numbers that are in *either* set RR *or* set TT, and put them together in one new set. Watch out! Don't mix up union with intersection!
Union means "everything in both", while intersection means "only what's in common".
Also, don't include duplicates!
Each number should appear only once in the final set.

STEP 2

1. Combine the sets

STEP 3

The symbol \cup means *union*.
Taking the union of two sets means we're creating a new set that contains *all* the elements present in *either* of the original sets.
Think of it like combining your friend's toy collection with yours – now you have all the toys!

STEP 4

Set RR has the following elements: 22, 66, 77, and 88.

STEP 5

Set TT has the following elements: 33, 44, and 55.

STEP 6

Let's put all the numbers from both sets together: 22, 66, 77, 88, 33, 44, and 55.

STEP 7

While not strictly necessary, ordering the elements numerically makes it easier to read and compare with the answer choices: 22, 33, 44, 55, 66, 77, and 88.
This forms our new set RTR \cup T.

STEP 8

The union of sets RR and TT is RT={2,3,4,5,6,7,8}R \cup T = \{2, 3, 4, 5, 6, 7, 8\}.
This matches answer choice **B**.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord