Determine the cardinality of each other following sets Prove

Determine the cardinality of each other following sets. Prove your answer.

a) [0,1] U [2,3]

b) R x R

I\'m very confused about cardinality with cross products and unions and such. Please help!

Solution

a) [0,1] represents the interval between 0 and 1 and hence contains infinite elements

Similarly [2,3] includes all values between 2 and 3.

Hence their union will be infinite and continuous not countable.

b) RxR will be of the form (x,y) where x and y are real.

This also infinite and not countable.