Define relation R as follows: xRy if x and y are bit strings with |x| >= 2 and |y| >= 2 such that x and y agree in their first two bits. Show that R is an equivalence relation. Construct the equivalence classes for R.
Reflexive? Let x=y. Then xRx, since x is a bit string with cardinality >= 2, and agrees in its own first two bits.
Symmetric? Yes, because the conditions are not dependent on order. If xRy then yRx just as well.
Transitive? Indeed; if xRy and yRz, then x, y, and z are all bit strings with cardinality >= 2 with the same first two bits. Therefore xRz.
But to construct the equivalence classes, I don't even know where to start =\