Solved Examples on Set Symbols
Example 1: Given two sets with P={21, 32, 43, 54, 65, 75} and Q={21, 43, 65, 75, 87, 98} what is the value of P∪Q?
Answer:
P={21, 32, 43, 54, 65, 75} and Q={21, 43, 65, 75, 87, 98}
P∪Q={21, 32, 43, 54, 65, 75, 87, 98}
Example 2: What is the value of |Y| if Y={13, 19, 25, 31, 42, 65}?
Answer:
|Y| = Cardinality of the set=number of elements in the set is the solution.
|Y| = n(Y)=6, since the set Y has 6 elements.
Example 3: Given two sets with values P={a,c,e} and Q={4,3}, determine their Cartesian product.
Answer:
Cartesian product = P × Q
If P={b, d, f} and Q={5, 6}
Then P × Q={(b,5), (d,6), (b,5), (d,6), (b,5), (d,6), (b,5), (d,6), (b,5), (d,6)}
Example 4: Assume P = {x: x is a natural integer and a multiple of 24, and Q = {x: x is a natural number smaller than 8}. Determine P ∪ Q.
Answer:
Given that
P = {1, 2, 3, 4, 6, 8, 12, 24}
Q = {1, 2, 3, 4, 5, 6, 7}
As a result, P ∪ Q = {1, 2, 3, 4, 5, 6, 7, 8, 12, 24}
Example 5: Assume P = {3, 5, 7}, Q = {2, 3, 4, 6}. Find (P ∩ Q)’.
Answer:
Given, P = {4, 6, 8}, Q = {3, 4, 5, 7}
P ∩ Q = {4}
Therefore,
(P ∩ Q)’ = {3, 5, 6, 7, 8}
Example 6: If P = {4, 5, 7, 8, 9, 10} and Q = {3, 5, 7, 9, 12, 14}, determine
(i) P-Q and (ii) P-Q.
Answer:
Given,
P = {4, 5, 7, 8, 9, 10} and Q = {3, 5, 7, 9, 12, 14}
(i) P – Q = {4, 8, 10}
(ii) Q – P = {3, 12, 14}
Set Symbols
Set Symbols are a collective term used for all the symbols used in set theory which is the branch of mathematics that deals with the collection of objects and their various properties. A set is a well-defined collection of objects where each object in the collection is called an element and each element of the set follows a very specific rule. Generally, capital letter of English alphabets are used to denote sets and some letters denotes some specific sets in set theory.
There are many symbols used throughout the study of this branch of math, some of the common symbols are {}, |, :, ∈, ∉, ⊆, U, Ø, etc. We will discuss all these symbols in detail in the article including the history of these symbols as well. So, let’s start our journey of learning about various different set symbols used in set theory.
Table of Content
- What are Set Symbols?
- History of Set Symbols
- Basic Concepts of Set Symbols
- Set Symbols in Maths
- Set Theory Symbols
- Solved Examples on Set Symbols
- Practise Qusetion for Set Symbols
- FAQs