Ifa is an uncountable set andb is a countable set. musta ? b be uncountable?

Solution:Step 1: In the given problem we have to prove that if a is an uncountable set and b is a countable set. Must a b be uncountableStep 2: We have two sets a and bConsider b is countable then we can represent the elements {b1 b2 b3…...bn} but a is the uncountable set so it keeps infinite elements.Now for each set we have to find whether each set is finite, countably infinite, or uncountable.Example: Countably infinite: Integers which are multiple of 5 0,5,-5,10,-10…………. Uncountable: the real number between 5 and 6