Let S={(x1,0):x1∈R}S=\{(x_1,0):x_1\in\mathbb{R}\}S={(x1,0):x1∈R} and T={(0,x2):x2∈R}T=\{(0,x_2):x_2\in\mathbb{R}\}T={(0,x2):x2∈R}. Which of the following is correct?
S,TS,TS,T and S∩TS\cap TS∩T are vector spaces
S,TS,TS,T and S∪TS\cup TS∪T are vector spaces
S∪TS\cup TS∪T and S∩TS\cap TS∩T are vector spaces
Neither S∪TS\cup TS∪T nor S∩TS\cap TS∩T is a vector space
