Q. Answer true or false :
a. Every subset of an infinite set is infinite.
  explain your answer with proof?

Asked by imabhi264 | 8th Jul, 2017, 05:17: PM

Expert Answer:

begin mathsize 16px style Let space straight A space be space an space infinite space set. space Take space some space element space of space straight A space say space it space straight a subscript 1.
he space set space straight A minus open curly brackets straight a subscript 1 close curly brackets space is space not space empty semicolon space denote space one space element space of space its space be space straight a subscript 2.
This space process space may space continue space indefinitely comma space at space the space straight n to the power of straight h space stage space the space set
straight A minus open curly brackets straight a subscript 1 comma straight a subscript 2 comma...... straight a subscript straight n minus 1 end subscript close curly brackets
cannot space be space empty space setsince space straight A space is space infinite. space The space set space open curly brackets straight a subscript 1 comma straight a subscript 2........... close curly brackets
is space straight a space countably space infinite space subset space of space straight A.

end style

Answered by Sneha shidid | 8th Jul, 2017, 09:57: PM