Ass 2.3 Parity Question Exclusive Or P Q T T F T F T F T T F F F PeQ Connector Exclusive-Or (POQ): One has be true but not both. P and Q have the opposite values. Parity (POQO...OR): The number of true variables is odd. Boolean Addition: 1+0+1+1+0 =modz 1 Define Tz = xx20x20...Oxn, Tin = TOT, and 0,=t vaz. 1. Tn is true when the # of true variables is odd. Similarly, explain for which T/F settings of the x; variables is Tin true. 2. For which is O, true? Explain. 3. Which are the following are tautologies? For each prove it using the previous ones. a) La iff aoT b) a v aOT c) , n Ass 2.3 Parity Question Exclusive Or T T F T F T F F T T F F F PQ Connector Exclusive-Or (P+Q): One has be true but not both. P and Q have the opposite values. Parity (POQO...OR): The number of true variables is odd. | Boolean Addition: 1+0+1+1+0 =mod2 1 Define ten = x20x20x20...Ox tn=rOT, and 0,=VIN. 4. If you set x, to be F/T, what do tih, T, and 0, simplify to? Explain. F T th 5. What does the DP tree be for O, look like? In How deep is each path and xn . how many leaves does it have? F T Explain. *n-1 Simplify On What is the moral? FT Xn-2 X, n-2 F F F' set xn in n Xn-1 Xn-2 Xn-2 FAT Ass 2.3 Parity Question Exclusive Or P Q T T F T F T F T T F F F PeQ Connector Exclusive-Or (POQ): One has be true but not both. P and Q have the opposite values. Parity (POQO...OR): The number of true variables is odd. Boolean Addition: 1+0+1+1+0 =modz 1 Define Tz = xx20x20...Oxn, Tin = TOT, and 0,=t vaz. 1. Tn is true when the # of true variables is odd. Similarly, explain for which T/F settings of the x; variables is Tin true. 2. For which is O, true? Explain. 3. Which are the following are tautologies? For each prove it using the previous ones. a) La iff aoT b) a v aOT c) , n Ass 2.3 Parity Question Exclusive Or T T F T F T F F T T F F F PQ Connector Exclusive-Or (P+Q): One has be true but not both. P and Q have the opposite values. Parity (POQO...OR): The number of true variables is odd. | Boolean Addition: 1+0+1+1+0 =mod2 1 Define ten = x20x20x20...Ox tn=rOT, and 0,=VIN. 4. If you set x, to be F/T, what do tih, T, and 0, simplify to? Explain. F T th 5. What does the DP tree be for O, look like? In How deep is each path and xn . how many leaves does it have? F T Explain. *n-1 Simplify On What is the moral? FT Xn-2 X, n-2 F F F' set xn in n Xn-1 Xn-2 Xn-2 FAT