Math Problem Statement
Determine the complements of sets Q and R within the universal set P, given the following sets: P = {x | x is an alphabet}, Q = {d, e, f, g}, and R = {a, e, i, o, u}.
Solution
The image presents a mathematics or set theory problem in Indonesian. Here's a breakdown of the key points:
- The title of the slide is "Komplemen" (Complement in English).
- The problem involves three sets:
- P = {x | x is a letter or alphabet character} (P represents the set of all alphabet letters).
- Q = {d, e, f, g}
- R = {a, e, i, o, u}
- The task is to determine the complements of sets Q and R within the universal set P.
Steps:
-
Complement of Q:
- The complement of a set consists of all elements in the universal set P that are not in Q.
- So, Q' (complement of Q) = P - Q = {all letters except d, e, f, g}.
-
Complement of R:
- Similarly, the complement of set R is all the letters in P that are not in R.
- R' (complement of R) = P - R = {all letters except a, e, i, o, u}.
Would you like me to proceed with detailed calculations for these complements? Let me know if you have any questions!
5 Related Questions:
- What is the general formula for finding the complement of a set?
- Can a set have more than one complement depending on the universal set?
- How does the intersection of complements relate to De Morgan's laws?
- What are the differences between complement and subset in set theory?
- Can you determine the complement of a set using a Venn diagram?
Tip:
Always ensure you clearly define the universal set when working with complements, as this directly affects the outcome!
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Math Problem Analysis
Mathematical Concepts
Set Theory
Complement of Sets
Formulas
Q' = P - Q (Complement of Q)
R' = P - R (Complement of R)
Theorems
Set Complement
Suitable Grade Level
High School