Suppose you know that ui$(\backslash$sigma i$,\backslash$Theta $-$i$)=5$ for a particular mixed strategy $\backslash$sigma i in Si and belief $\backslash$Theta $-$i in $\backslash$Delta S$-$i$.$ Must it be true that there is a pure strategy si in Si such that ui $($si $,\backslash$Theta $-$i $)>=5?$ Prove this or find an example showing that the statement is false.