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| 1 | +Homework 3: Simplify expressions |
| 2 | + |
| 3 | + |
| 4 | + |
| 5 | +T && T && F && T |
| 6 | +- F [as all of them are && and one of them is F] |
| 7 | +======================================================================== |
| 8 | + |
| 9 | +T && T && F && T || T && T |
| 10 | +- T && T && F && T ==> Reduce to F |
| 11 | +- F || T ==> T |
| 12 | +======================================================================== |
| 13 | + |
| 14 | +T && T && T && T || T && (T || F) |
| 15 | +- (T || F) ==> Reduce to T |
| 16 | +- T && T && T && T || T && T |
| 17 | +- T && T && T && T ==> reduce to T |
| 18 | +- T || T && T |
| 19 | +- T && T ==> Reduce to T |
| 20 | +- T || T ==> T |
| 21 | +======================================================================== |
| 22 | + |
| 23 | +T && T && T || T && (F || (T && (T && T))) |
| 24 | +- (T && T) ==> reduce to T |
| 25 | +- T && T && T || T && (F || (T && T)) |
| 26 | +- (T && T) ==> reduce to T |
| 27 | +- T && T && T || T && (F || T) |
| 28 | +- (F || T) ==> reduce to T |
| 29 | +- T && T && T || T && T |
| 30 | +- T && T && T ==> reduce to T |
| 31 | +- T || T && T |
| 32 | +- T && T ==> reduce to T |
| 33 | +- T || T ==> T |
| 34 | +======================================================================== |
| 35 | + |
| 36 | +T && T || T && F && T || T && T && F || (T && (T || F)) |
| 37 | +- (T || F) ==> reduce to T |
| 38 | +- T && T || T && F && T || T && T && F || (T && T) |
| 39 | +- (T && T) ==> reduce to T |
| 40 | +- T && T || T && F && T || T && T && F || T |
| 41 | +- T && T ==> reduce to T |
| 42 | +- T || T && F && T || T && T && F || T |
| 43 | +- T && F && T ==> Reduce to F |
| 44 | +- T || F || T && T && F || T |
| 45 | +- T && F && T ==> Reduce to F |
| 46 | +- T || F || T && T && F || T |
| 47 | +- T && T && F ==> Reduce to F |
| 48 | +- T || F || F || T ==> T |
| 49 | +======================================================================== |
| 50 | + |
| 51 | +T && T || T && F && T || T && T && F || (T && (T || F)) |
| 52 | +- (T || F) ==> reduce to T |
| 53 | +- T && T || T && F && T || T && T && F || (T && T) |
| 54 | +- (T && T) ==> reduce to T |
| 55 | +- T && T || T && F && T || T && T && F || T |
| 56 | +- (T && T) ==> reduce to T |
| 57 | +- T || whatever = T [smart reduction] |
| 58 | +======================================================================== |
| 59 | + |
| 60 | +T && T || T && F && T || (T && T && F || (T && (T || F))) |
| 61 | +- Notice T && T || something = T, so we know the answer T |
| 62 | +======================================================================== |
| 63 | + |
| 64 | +(T && T || T && F && T || T) && T && F || (T && (T || F)) |
| 65 | +- (T && (T || F)) ==> reduced in 2 steps to: T |
| 66 | +- (T && T || T && F && T || T) ==> (T || F || T) ==> T |
| 67 | +- So now is: |
| 68 | +- T && T && F || T ==> F || T ==> T |
| 69 | +======================================================================== |
| 70 | + |
| 71 | + |
| 72 | +T && T || T && (F && T || T && T) && F || (T && (T || F)) |
| 73 | +- (T && (T || F)) ==> reduced in 2 steps to: T |
| 74 | +- (F && T || T && T) ==> (F || T) ==> T |
| 75 | +- T && T || T && T && F || T ==> T || F || T = T |
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