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### Question

- All rational numbers are integers, but not vice versa.
- All integers are irrational numbers, but not vice versa.
- √2 is an integer.

If the first two statements are true, the third statement is:

**A**

true.

**B**

false.

**C**

uncertain.

**D**

None.

**Soln.**

**Ans: c**

√2 is an irrational number, which is a known fact. On the basis of the truth of the first two statements, we have to test: "Is an irrational an integer?" If you try to draw a Venn diagram you will get three concentric circles. Rational inside Integer and the Integer inside Irrational, which means that there are some irrationals that are integers, and some that are not. Hence the answer should be "uncertain".