Option D) The set of real numbers between 0 and 1/2 is countable. is not true.
A set is countable if we can say what is the nth element going to be. For example set of negative integer, we know that first element will be -1, and 5th element will be -5 and nth element will be -n. Similarly we can for multiple of 7 and even number too.
But we can not do the same for real number. Because there is infinite real between (o and 1/2). There is a theorem which state that if P and Q are real then (P+Q)/2 will always be a real number. This theorem can be used to prove that there are infinite many real number between any two real number.
