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We are familiar with basic algebraic operations. These basic mathematical operations, however, are not valid in all contexts. For example, algebraic operation such as addition has different details, when operated on vectors. Clearly, we expect that these operations will also be not same in the case of sets – which are collections and not individual elements.

Nevertheless, set operations bear resemblance to algebraic operation. For example, when we combine (not add) two sets, then the operation involved is called “union”. We can see that there is resemblance of the intent of addition, subtraction etc in the case of sets also.

Venn diagrams

Venn diagrams are pictorial representation of sets/subsets and relationship that the sets/subsets have among them. It helps us to analyze relationship and carry out valid set operations in a relatively easier manner vis – a – vis symbolic representation.

Universal set

Universal set is the largest set among collection of sets. Importantly, it is not the collection of everything as might be conjectured by the nomenclature. For example, "R", is universal set comprising of all real numbers. The rational numbers, integers and natural numbers are its subset. In other consideration, we can call integers as universal set. In that case, sets such as {1,2,3}, prime numbers, even numbers, odd numbers are subset of the universal set of integers.

The universal set is pictorially represented by a region enclosed within a rectangle on Venn diagram. For illustration, consider the universal set of English alphabets and universal set of first 10 natural numbers as shown in the top row of the figure

Universal set

The universal set is represented by a region enclosed within a rectangle.

Many times, however, we may not be required to list elements of a universal set. In such case, we represent the universal set simply by a rectangle and the symbol for universal set, “U”, in the corner. This is particularly helpful, where number of elements in universal set are very large.

The subsets of the universal set are represented by closed curves – usually circles. The subset of vowels (V) is shown here within the circle with the listing of elements. Note that we have not listed all the alphabets for universal set and used the symbol “U” in the corner only.

Subset

The subset of the universal set is represented by a closed curve – usually circle.

Union of sets

Union works on two operands, each of which is a set. The operation is denoted by symbol " ". Now, the question is : what do we expect when two sets are combined? Clearly, we need to enlist all the elements of two sets in the resulting set.

Union of two sets
The union of sets “A” and “B” is a third set, which consists all the elements of two sets.

In symbol,

A B = { x : x A o r x B }

The word “or” in the set builder form defining union is important. It means that the element “x” belongs to either “A” or “B”. The element may belong to both sets (common to two sets), but not necessarily. We can, therefore, infer that union set consists of :

Questions & Answers

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
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ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
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Jonathan
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Jonathan
generally amnesi how long yrs memory loss
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interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
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Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
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Jharna
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Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
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Source:  OpenStax, Functions. OpenStax CNX. Sep 23, 2008 Download for free at http://cnx.org/content/col10464/1.64
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