$R$ and $S$ are equivalence relations on $A$. Define relation $T=\{(x,y,z,t)\in R\times S : xRt \Rightarrow ySz\}$ on $A^2$. Check $T$ is equivalence relation or not.
I am in it is not reflexive. For it can be reflexive I need to prove followings.
For any $(x,y)\in A^2$, $(x,y,x,y)\in T$ i.e. $xRy\Rightarrow ySx$
I cannot see how can I prove or disprove this. Thank you so much for any help.