1. Let A be an uncountable set, and let B be a countable set. Show that...

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1. Let A be an uncountable set, and let B be a countable set. Show that A is equivalent to AUB. (No relation between A and B is assumed here) 2. Show that the Cantor set A contains no (non-empty) open interval. (Hint: Show that if x,y EA with then there exists some z E [0, 1] \ A so that x < z 1. Let A be an uncountable set, and let B be a countable set. Show that A is equivalent to AUB. (No relation between A and B is assumed here) 2. Show that the Cantor set A contains no (non-empty) open interval. (Hint: Show that if x,y EA with then there exists some z E [0, 1] \ A so that x < z