Identify the true statements in the following:

Question

\[\](1)If a curve is symmetrical about the origin, then it is symmetrical about both axes.\[\](2)If a curve is symmetrical about both  the  axes, then it is symmetrical about the origin.\[\](3)A curve f(x,y)=0 is symmetrical about the line y=x if f(x,y)=f(y,x).\[\](4)For the curve f(x,y)=0, if f(x,y)=f(-y,-x),then  it  is symmetrical about the origin.