Question

Consider the following statements:
$S_1:ThereexistinfinitesetsA,B,Csuchthat$
$A\cap (B\cap C)isfinite.$
$S_2$:
There exist two irrational numbers x and y such that (x+y) is rational.
Which of the following is true about
$S_{1}and$ $S_2$ ?

• A. $Only{S}_{2}iscorrect$
• B. $Noneof{S}_{1}and$ $S_{2}iscorrect$
• C. $Both{S}_{1}and$ $S_{2}arecorrect$
• D. $Only{S}_{1}iscorrect$

Answer 1

The correct option is C $Both{S}_{1}and$ $S_{2}arecorrect$

$S_1:$
Let A= set of integers
B= set of odd integers
C= set of even integers
$A\cap (B\cap C)=\varphi$ $and\varphi isfiniteset.$
Therefore, $S_1$ is true.

$S_2:$
Let two irrational number x and y are respectively
$(1+\sqrt{2})and$ $(1-\sqrt{2})$
$sox+y=1+\sqrt{2}+1-\sqrt{2}$
=2 which is rational number
Therefore, $S_2$ is true. Since both $S_1$ and $S_2$ are true, option (c) is true.