$$3$$ and $$4$$

$$2$$ and $$3$$

$$1$$ and $$2$$

$$1,2$$ and $$4$$

each system in the cascade is individually casual and unstable

at least one system is unstable and atleast one system is casual

at least one system is casual and all systems are unstable

the majority are unstable and the majority are casual

$$y\left( t \right)$$

$$y\left( {2\left( {t - \tau } \right)} \right)$$

$$y\left( {t - \tau } \right)$$

$$y\left( {t - 2\tau } \right)$$

$$y\left( n \right)$$ is non causal with finite support

$$y\left( n \right)$$ is causal with infinite support

$$y\left( n \right)$$ $$ = 0;\,|n| > 3$$

$$\eqalign{ & {\mathop{\rm Re}\nolimits} {\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}} = - {\mathop{\rm Re}\nolimits} {\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}}; \cr & {\rm I}m{\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}}\, = {\rm I}m{\left[ {Y\left( z \right)} \right]_z} = {e^{j0}};\,\, - \pi \le \theta < \pi \cr} $$