SOLUTION: ≡ Mod 2 ∩ ≡ Mod 3 Is an equivalent relation on Z? ≡ Mod 2 ∪ ≡ Mod 3 Is an equivalent relation on Z? I think ≡ 2 ∩ ≡ 3 it is. ≡ 2 ∩ ≡ 3 = ≡6, and �

Question 1196070: ≡ Mod 2 ∩ ≡ Mod 3 Is an equivalent relation on Z?
≡ Mod 2 ∪ ≡ Mod 3 Is an equivalent relation on Z?
I think
≡ 2 ∩ ≡ 3 it is.
≡ 2 ∩ ≡ 3 = ≡6, and ≡6 it's an equivalent relation on Z.
but I don't understand ≡2 ∪ ≡3 please explain. Thanks
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.
≡ Mod 2 ∩ ≡ Mod 3 Is an equivalent relation on Z?

~~~~~~~~~~~~~~~

        Wording in your post is strange and incorrect.
        The correct wording for the first part question would be

                    ≡ Mod 2 ∩ ≡ Mod 3 is equivalent to which relation on Z?

In my post, I will answer part 1 in this formulation.

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.

Part 1 is complete.

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