Cross product and dot product relationships

The question is the form of true or false

If $\displaystyle \underline a \bullet \underline b = \underline a \bullet \underline c $ then $\displaystyle \underline b = \underline c $

The answer is given as false, I cannot understand why though. If the dot product of lhs and rhs equal each other and they share vector a in the calculation of the dot product how can vector b and c not equal each other ?

and similarly for if $\displaystyle \underline a \times \underline b = \underline a \times \underline c $ then $\displaystyle \underline b = \underline c $

why does b not equal c in this case aswell?