Write a regular expression to denote the set of all strings of letters that contain the five vowels in order. Assume that letters can only be lower case. Then, re-state the regular expression in terms of a context free grammar. So to be clear, the vowels will only appear 1 time and in order, i. e. a will be before e, e will be before i, i will be before o, and o will be before u. The other letters may or may not appear at all and can be before, in between, or after the vowels.

:you areto design the controller for alight that functions both as an ordinary light and also as a motion activated light and alarm. a.if the manual switch s is on, then the light l is on. b.besides the manual switch, there is a motion detector, m1, which activatesthis light.c.if motion is detected but the light is on anyway because s is on, only then a secondoutput a, an alarm, is turned on. d.the disable switch, d, disables the motion activated light and alarmbut leaves manual control operation of the light using switch s.(i)read the problem statement and clearly identify the inputs and outputs for the circuit you are designing. (ii)create the truth table for this system; include the light, alarm, switch, disable, and the motion sensor.(iii)draw a schematic of this system.