Symmetric and asymmetric preferences I encountered a question where it was given that the consumers had asymmetric preferences. I couldn't find the definition of the term in any of the microeconomics book available to me.

Can anybody explain the terms and the difference between symmetric and asymmetric preferences? Please!
It is just a strict preference relation, an asymmetric (generic) relation $\succ$ is such that $a \succ b \implies \lnot b \succ a$. 
With respect to symmetric preferences there are not really  pure symmetric ones in consumer theory at least, the only symmetric relation is total indifference ~ over the whole choice set. Clearly a ~b implies b ~a. A typical $\succeq$ preference relation is the union of an asymmetric and symmetric part.