Syllogism Quantifier Mix – UGC NET Question

The first statement says that all rational numbers are contained within the set of real numbers. The second statement tells us that there is at least some overlap between real numbers and integers. From these premises we can be sure that the set of rationals lies inside the reals, but we are not given an explicit link between rationals and integers. It is therefore safe to say that some real numbers may be rational numbers, since rational numbers form a subset of the reals.

Option A:
Option A, “Some integers are rational numbers,” is true in standard mathematics but does not follow solely from the given premises, which never state a direct relation between integers and rationals.

Option B:
Option B, “Some rational numbers are integers,” is also mathematically true but again goes beyond the information explicitly stated in the premises, which only connect rationals with reals and integers with reals.

Option C:
Option C cautiously asserts a possibility: since all rationals are reals, it is entirely consistent that some real numbers may be rational. This conclusion remains within what is warranted by the premises.

Option D:
Option D, “All integers are rational numbers,” is stronger than anything that can be deduced from the given statements and is not logically enforced by them, even though it is true in standard number systems.