Find the complement of the following expressions: (a) xy'+x'y (c) z+z'(v'w+xy) (b) (a+c) (a+b') (a' +b+c')

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4. A decorative display uses inexpensive mass produced colored lights having constant failure rate of 1000 per million per day. Assume that such a display is designed with 2000 such lights that are all turned on at the same time. The lights are so connected that failure of one does not affect the operation of others. a) How many lights can be expected to still be operational after 90 days? b) Determine the mean time to failure of any given light. c) Determine the probability that any given light will fail within the first 100 days after turn on and also that 20 lights will do likewise. d) Repeat part c) replacing 1000 days for 100 days. e) Determine the time that can be expected to elapse (from turn on) before the display has only one operational light left.

In relation to ”smart grid”, discuss the attributes that make the gridsmart.