Consider R^2 with the usual topology. Which of the following statements are TRUE for all A, B ⊆ R^2? P: {A ∪ B}↖ {———} = A↖{—} ∪ B↖{—} Q: {A ∩ B}↖ {———} = A↖{—} ∩ B↖{—} R: (A ∪ B)^˚ = A^˚ ∪ B^˚ S: (A ∩B)^˚ = A^˚ ∩ B^˚

Question

Consider R^2 with the usual topology. Which of the following statements are TRUE for all A, B ⊆ R^2?    P: {A ∪ B}↖ {———}  = A↖{—} ∪ B↖{—}  Q: {A ∩ B}↖ {———}  = A↖{—} ∩ B↖{—}  R: (A ∪ B)^˚  = A^˚ ∪ B^˚  S: (A ∩B)^˚   = A^˚ ∩ B^˚

Examsnet · Accepted Answer

Correct Answer is :  P and S only

GATE Mathematics 2013 Paper