DM/ Set Problem

Question

S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite.

S2: There exists two irrational numbers x and y such that (x+y) is rational.

Which of the following is true about S1 and S2?

(A) Only S1 is correct and S2 is incorrect

(B) Only S2 is correct and S1 is not correct

(C) S1 and S2 both are correct

(D) S1 and S2 both are not correct

(E) If you think any other options.

Comments

S2: There exists two irrational numbers x and y suchthat (x+y) is rational.

Answer 1

S1- There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite.

Ans- Correct 

Ex- A- set of all odd number 

      B- set of all negative even number

      C- set of all positive even number 

  A ∩ ( B U C) = ∅  ( finite set )

S2-  There exists two irrational numbers x and y suchthat (x+y) is rational.

 Ans- Correct.

Let X= 2 + $\sqrt{2}$    // irrational no.

        Y = 2 - $\sqrt{2}$    // irrational no.

X + Y = 4   // rational no.

Answer 2

1.A = set of odd numbers, B = set of even positive numbers, C = set of even negative numbers.

Here A, B and C are infinite sets, but A∩(B U C) is ∅ which is finite.

2. : x =1+⎷2 y=1-⎷2x and y are irrational, but x+y is 2, which is rational.

So both S1 and S2 are correct.