Working on Homotopy Equivalent Suppose I have spaces $X_{0}, X_{1},Y_{0},Y_{1}$ and $X_{0}$ is homotopy equivalent to $Y_{0}$ and $X_{1}$ is homotopy equivalent to $Y_{1}$.
I would like to show that $X_{0}$ x $X_{1} $ is homotopy equivalent to $Y_{0}$ x $Y_{1} $.
How do I approach this statement? I am fresh new to this topic so any input will be greatly appreciated.
Thanks!

acord your homotopy you to functions f0 and f1 and g0 g1 and g0(f0) in X0 and(g1(f1)) in X1 are nullhomotopys. I try to take the function f:=(f0,f1) and g:=(g0,g1) so g(f)=(g0(f0),g1(f1)) is nullhomotopy in X0*X1.
