Can you please show all work and explanation.

\#5 Perform two-level logic size optimization for F(a,b,c,d)=abc+abcd+abd using a k-map. Write the final function two ways: sum of minterms and minimal SOP. \#6 Perform two-level logic size optimization for F(a,b,c,d)=abcd+abcd, assuming a and b can never both be 1 at the same time and that c and d can never both be 1 at the same time. Treat all of these situations as don't cares. Write the final function in minimal SOP form. Instructions for Problems 7 and 8: Minimize the circuit. Use algebra, k-maps, and other means (factoring, other gates, shared gates, etc). Name the bits for each input as you want. Typical choices are ABC, wxyz, P4 P3 P2 P1 PO, etc. \#7 A museum has three rooms, each with a motion sensor (m0,m1, and m2) that outputs 1 when motion is detected. At night, the only person in the museum is one security guard who walks from room to room. Create a circuit that detects whether the guard is properly patrolling the museum, detected by exactly 1 motion sensor being 1 . (If no motion sensor is 1 , the guard may be sitting, sleeping, or absent.) Start with a truth table. Assign the output to A, where 1 means correct patrol. \#8 A car has a fuel-level detector that outputs the current fuel-level (0-7) as a 3-bit binary number, with 000 meaning empty and 111 meaning full. Create a circuit that illuminates a "low fuel" indicator light (by setting an output L to 1 ) when the fuel level drops below level 3