A **Venn Diagram** is a way to visualize set relations between a finite number of sets. Below is a Venn Diagram for three sets \(T, D,\) and \(H\).

## We introduce some notation from Set Theory:

\( |T|\) is the number of elements in set \( T\).

Intersectionof two sets, denoted \( \cap\), refers to the elements that are in both sets. In the example, \( T \cap D = \{ d, g\} \).

Unionof two sets, denoted \( \cup\), refers to the elements that are in at least one of the two sets. In the example, \( T \cup H = \{a, c, d, e, f, g\} \).

Complement (Absolute), denoted \( ^c\), refers to the elements that are not in the set. In the example, \( D^c = \{ a, c, e, i\} \).

Complement (Relative), denoted \( \backslash\), refers to the elements in the first set, but are not in the second set. In the example, \( H\backslash T = \{ c, f \} \).

Symmetric Difference, denoted \( \triangle\), refers to the elements that are in at least one of the two sets, but are not in both sets. In the example, \( D \triangle H = \{b, c, d, e\} \).

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## Comments

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TopNewestH\T can also be written H - T.

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Ya ......dear right

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As a non-mathematician I found some of the thinking in these examples quite puzzling and hard to follow!

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Complement of H = H'

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this is kinda like logic gates

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Enlightening

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how do you solve when there is an unknown is a given set?

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You need to turn the rules into English and use logic. Like in the question that you probably came from, it says that: 0 is in the set. If \(p\) is in the set, and \(q\) is in the set, and \(p \neq q\), then \(p+q\) is in the set. Now, if 10 is in the set, then -10 being in the set wouldn't break any rules, becuase \(-10 \neq 10\) and \(-10+10=0\) which is also in the set.

Set notation isn't

usefulin problem solving, but it helps show the question in a short way. Imagine if we didn't have any math symbols. Then \(3x-9= 0, x=3\) would be: "Take a number. If you take away nine from 3 times that number the answer is zero. The number is 3." Which is easier to understand?Log in to reply

yeah,, idont find this post useful in solving,, please how do you actually solve???

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