From Wikipedia, I noticed that the wedge sum is the quotient topology of the disjoint union of two spaces, namely
$$X\vee Y = (X\sqcup Y)/\sim$$
by the identification $$x_0 \sim y_0$$
My question is: Is the wedge sum of any two hausdorff spaces hausdorff? How can I prove/disprove such a claim? I'm not super familiar with what happens to neighborhoods in the disjoint union.
Sorry if my english isnt great
