Question 1196070
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≡ Mod 2 ∩ ≡ Mod 3 Is an equivalent relation on Z?


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        Wording in your post is strange and incorrect.

        The correct wording for the first part question would be


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                    ≡ Mod 2 ∩ ≡ Mod 3 is equivalent to which relation on Z?
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In my post, I will answer part 1 in this formulation.



<pre>
Relation  ≡ Mod 2 ∩ ≡ Mod 3  is equivalent to relation  ≡ Mod 6.


In human language, those integers that are multiple of 2 and are multiple of 3 simultaneously are those and only those that are multiple of 6.
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Part 1 is complete.