4.2 A flow rate sensing device used on a liquid transport pipeline functions as follows. The device provides a 5-bit output where all five bits are zero if the flow rate is less than 10 gallons per minute. The first bit is 1 if the flow rate is at least 10 gallons per minute; the first and second bits are 1 if the flow rate is at least 20 gallons per minute; the first second, and third bits are 1 if the flow rate is at least 30 gallons per minute; and so on. The five bits, represented by the logical variables A, B, C, D, and E, are used as inputs to a device that provides two outputs Y and Z. (a) Write an equation for the output Y if we want Y to be 1 iff the flow rate is less than 30 gallons per minute. (b) Write an equation for the output Z if we want Z to be 1 iff the flow rate is at least 20 gallons per minute but less than 50 gallons per minute. 4.7 Each of three coins has two sides, heads and tails. Represent the heads or tails sta- tus of each coin by a logical variable (A for the first coin, B for the second coin, and C for the third) where the logical variable is 1 for heads and 0 for tails Write a logic function F(A,B,C) which is 1 iff exactly one of the coins is heads after a loss of the coins. Express F (a) as a minterm expansion. (b) as a maxterm expansion.