1. Simplify, using algebraic manipulations, the following Boolean expressions to a mini- mum number of terms and factors (a) XYZ +XY+XYZ (b) XYZ+ XZ 2. Find the complement of the following expression (a) A = XY + XY 3. Using DeMorgan's Theorem, express the following function (a) F- XY +XY +YZ with only OR and complement operations (hint: use, the property: F-F) 4. Simplify the following expressions by means of a three-variable K-Map (a) XY +YZ+ X Y Z 5. Simplify the following expressions by means of a four-variable K-Map (a) AD + BD BC + ABD (b) ABC + CD + BCD + BC 6. Propose and solve your own boolean expression problem-A 7. Heart-Rate Monitor A heart rate monitor measures an individuals heart rate and blood pressure. Both sensors output zero (0) if they are within safety range. An alarm will sound if either sensor indicates an unsafe condition is present Set-up the appropriate truth table, simplify using K-maps. Implement, using LogiSim, the simplified logic circuit with optimal number of logic gates 8. Hurricane Detector Three LEDs (one red, one green, one blue) turn on when a number 0-7 is passed through. Red turns on with even numbers, green turns on with odd numbers, blue turns on with multiples of 3. Zero means they are all off, seven means they are all on Set-up the appropriate truth table, simplify using K-maps. Implement, using LogiSim, the simplified logic circuit with optimal number of logic gates