Topic
Use the notation \( \subset \) to describe the relationship of two different sets in the following set: \(\left[ { – 1;3} \right];\left( { – 1;3} \right);\left[ { – 1;3} \right),\left( { – 1;3} \right],\left\{ { – 1;3} \right\}\)
Detailed explanation
We have:
[– 1; 3] = {x ℝ| – 1 x 3}
(– 1; 3) = {x ∈ ℝ| – 1 < x < 3}
[– 1; 3) = {x ∈ ℝ| – 1 ≤ x < 3}
(– 1; 3] = {x ℝ| – 1 < x ≤ 3}
{- first; 3}
Then we have:
(– 1; 3) [– 1; 3]; [– 1; 3) ⊂ [– 1; 3]; (– 1; 3] [– 1; 3]; {- first; 3} [– 1; 3].
(– 1; 3) [– 1; 3); (– 1; 3) ⊂ (– 1; 3].
