Is the formula (x∨y)∧(x- ∨ y)∧(x- ∨ y-) satisfiabl
Is the formula (x∨y)∧(x- ∨ y)∧(x- ∨ y-) satisfiable? Defend your answer:
•If this formula is satisfiable, give a satisfying truth assignment for x and y.
•If this formula is not satisfiable, give a proof that no satisfying assignment exists.
You can either use a truth table, or you can use the laws of Boolean algebra to simplify this expression to one that is obviously either satisfiable or non-satisfiable.
Homework Answers
Satisfiable means: By putting the value of X and Y in terms of the True and False. In any combination of the true and false the formula should give one true value. so let us put the combination of the true and false in X and Y position
Truth table:
True= T and False= F
X- is the complement of the X.
Truth table approach:
X Y (X V Y) (X- V Y) (X- V Y-) Final result
T T T T F F
T F T F T F
F T T T T T
F F F F F F
So for a combination of X= False And Y= True, the final formula which is AND operation of all the variables gives the True value, so the formula is satisfiable. But for some value, it is giving the false value so it is not a tautology.
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z')
( x
y'
z)
(w'
x
y')
(w'
x'
z)
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