For following determine whether statement is true or false. 1. Cardinality of an interval (0,10) is the same as cardinality of an interval (10,100)  2. Cardinality of the set of natural numbers is the same as cardinality of the set of integers 3. Cardinality of the set of natural numbers is smaller then cardinality of the set of rational numbers 4. Cardinality of an open interval (1,3) is the same as cardinality of a closed interval [1,3]  5. Cardinality of the set of integers is bigger than cardinality of an interval [1,2]

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Q: true or false and why ? The set [0,1] has the same cardinality as ℝ .

A: True. See the attachment

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.