Let X={1,2,3}X={1,2,3}. Let P(X)P(X) be the set of all subsets of XX (i. e. Power set of XX). Let RR be a relation defined on P(X)P(X) by the following. For all sets AA and BB in P(X)P(X), ARBARB iff |A|=|B||A|=|B|. Is RR an equivalence relation?

Yes

Step-by-step explanation:

For the equation to be equivalence then it must be

Reflexive, Symmetric and transitive

since |A|=|B|;  

Every element in A is in B then R is reflexive

If f(1) = g(1), then g(1) = f(1), so R is symmetric.

If f(1) = g(1) and g(1) = h(1), then f(1) = h(1), so R is transitive.

R is reflexive, symmetric, and transitive,

thus R is an equivalence relation.

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

idk

step-by-step explanation: