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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Enlightening

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this is kinda like logic gates

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

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

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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