Determine whether each of these compound propositions is satisfiable. (p union q

Question

Determine whether each of these compound propositions is satisfiable. (p union q union notof r) intersection (p union notof q union notof s) intersection (p union notof r union notof s) intersection (notof p union notof q union notof s) intersection (p union q union notof s) (notof p union notof q union r) intersection (notof p union q union notof s) intersection (p union notof q union notof s) intersection (notof p union notof r union notof s) intersection (p union q union notof r) intersection (p union notof r union notof s) (p union q union r) intersection (p union notof q union notof s) intersection (q union notof r union s) intersection (notof p union r union s) intersection (notof p union q union notof s) intersection (p union notof q union notof r) intersection (notof p union notof q union s) intersection (notof p union notof r union notof s)

Explanation / Answer

The truth table for each of expression is given by

1.

2.

3.

The truth table can be reffered for checking satisfiability of the expression.

P Q R S (-P) (-Q) (-R) (-S) (P and Q and (-R) P and (-Q) and (-S) P and (-R) and (-S) (-P) and (-Q) and (-S) P and (Q) and (-S) OR of 1 to 5 TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE False False False False False False TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE False False False False True True TRUE TRUE FALSE TRUE FALSE FALSE TRUE FALSE True False False False False True TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE True False True False True True TRUE FALSE TRUE TRUE FALSE TRUE FALSE FALSE False False False False False False TRUE FALSE TRUE FALSE FALSE TRUE FALSE TRUE False True False False False True TRUE FALSE FALSE TRUE FALSE TRUE TRUE FALSE False False False False False False TRUE FALSE FALSE FALSE FALSE TRUE TRUE TRUE False True True False False True FALSE TRUE TRUE TRUE TRUE FALSE FALSE FALSE False False False False False False FALSE TRUE TRUE FALSE TRUE FALSE FALSE TRUE False False False False False False FALSE TRUE FALSE TRUE TRUE FALSE TRUE FALSE False False False False False False FALSE TRUE FALSE FALSE TRUE FALSE TRUE TRUE False False False False False False FALSE FALSE TRUE TRUE TRUE TRUE FALSE FALSE False False False False False False FALSE FALSE TRUE FALSE TRUE TRUE FALSE TRUE False False False True False True FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE False False False False False False FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE False False False True False True

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