Assertion and reason: density

Exercise and reference answers

Questions

1. Reason

   Countless rationals lie between any two you pick.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   There is no next rational number after a given one.

2. Reason

   The mean of two rationals is itself rational and sits between them.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The mean is a reliable way to find a number in between.

3. Reason

   1 is the multiplicative identity.

   Verdict

   Both are true; the reason does not explain the assertion.

   Assertion

   Rationals are closed under multiplication.

Explanation