SHOW WORK! The cardinality of a set is the number of elements in the set. The un

Question

SHOW WORK!

The cardinality of a set is the number of elements in the set. The uncertainty ratio of a relation is |R:A rightarrow B|/|A Times B|. This quantity can be thought of as an informal measure of how the relation eliminates possible associations between elements of the two sets. The set Psi2 is the set of integer values that can be represented by a 39-bit C++ int variable, specifically Psi2 = {x Z | -(238) x (238 - 1)} Let R : Psi2 rightarrow Psi2 xRy x2 = y What is the cardinality of R (e.g. |R|)? What is the uncertainty ratio of R? Prove (or disprove) R is a function

Explanation / Answer

y^2 should also belong to the set psi 1 so max value of y is 2^19

so number of possible values of y are 2^20 (both +ve and -ve)

so cardinality of R is 2^20

  

b) |AxB| = 2^39 x 2^39 = 2^68

| R:a-->b| = 2^20

uncertainity ratio = 2^ -48

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