Q Consider the following statements: S1 ​: There exists infinite sets A,B,C…

Statement S1​:

There exist infinite sets A,B,C such that A∩(B∪C) is finite.

Example:

Let

A={1,2,3,… }

B={2,4,6,… }

C={−1,−2,−3,… }

Then A,B,C are infinite sets.

Now,

B∪C

contains positive even integers and negative integers.

Thus,

A∩(B∪C)={2,4,6,… } which is infinite.

But we can choose disjoint infinite sets:

Let

A={1,2,3,… }

B={−1,−2,−3,… }

C={−10,−11,−12,… }

Then,

A∩(B∪C)=∅ which is finite. Hence, S1 is true.

Statement S2:

Take

Both are irrational numbers.

But,

and 0 is rational.

Hence, S2​ is also true.

Therefore, both S1​ and S2​ are correct.