# Discrete mathematics cardinality using Richard Hammack's Elements of Discrete mathematics chapter 18 A superset of uncountable set is uncountable. (We say A is a superset of B if B sube A. )

Discrete mathematics cardinality using Richard Hammacks
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Raheem Donnelly
Consider A is a superset of B and A is uncountable. The objective to show that B is uncountable. Assume B is countable. Since using the concept that every subset of countable set is countable. So, A is countable. Which is contradiction, as given A is uncountable. Therefore, B is uncountable. $⇒$ a superset of uncountable set is uncountable. Hence proved.