$$\begin{aligned} & \mathrm { a } = \frac { \sqrt { 2 } } { 2 } \\ & \mathrm {~b} = \frac { \sqrt { 5 } } { 3 } \\ & \mathrm { c } = \frac { \sqrt { 7 } } { 4 } \end{aligned}$$
Which of the following orderings is correct for these numbers?
A) a $<$ b $<$ c
B) b $<$ a $<$ c
C) b $<$ c $<$ a
D) c $<$ a $<$ b
E) c $<$ b $<$ a