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Suyash Singh
Member advised that both problem statement and solution should be posted inline, not as images
Prove transitive (Relations and functions)
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In summary, the conversation is about a homework problem, specifically question 5 of an attached photo which involves equations and a proof involving a relation. The person responding suggests typing out the question and solution instead of making others strain to read a rotated photo.
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BvU
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Type the question. If you are too lazy to do that, then we are too lazy to break our neck trying to read something rotated over 90 degrees 
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Ray Vickson
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Suyash Singh said:
Type the question and (preferably) type the solution as well.
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BvU
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Hah, I didn't even get that far ...
...Related to Prove transitive (Relations and functions)
What does it mean for a relation to be transitive?
A relation is considered transitive if, for any three elements A, B, and C, if A is related to B and B is related to C, then A is also related to C. In other words, if A is connected to B and B is connected to C, then A is indirectly connected to C through the relationship.
How do you prove that a relation is transitive?
To prove that a relation is transitive, you must show that for any three elements A, B, and C, if A is related to B and B is related to C, then A is also related to C. This can be done by using a direct proof or a proof by contradiction. You must also make sure that the relation satisfies the reflexive and symmetric properties.
What is the importance of transitive relations in mathematics?
Transitive relations are important in mathematics because they allow us to make logical deductions and draw conclusions based on indirect relationships. This is especially useful in fields such as graph theory, set theory, and abstract algebra.
Can a relation be both transitive and symmetric?
Yes, a relation can be both transitive and symmetric. This type of relation is known as an equivalence relation. In an equivalence relation, elements are related to themselves (reflexive), related to each other in both directions (symmetric), and indirectly related through the relationship (transitive).
How is transitivity related to functions?
In functions, transitivity refers to the fact that if an input is related to an output, and the output is related to another output, then the input is also related to the second output. This is important because it allows us to compose functions and create more complex relationships between elements.
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