Check whether the compound proposition (p ∨￢q) ∧(q ∨￢r) ∧(r ∨￢p) ∧(p ∨q ∨r) ∧(￢p ∨￢q ∨￢r) is satisfiable or not?

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Using distribution property of and operators, the given proposition may be re-written as:

(p V((q) ∧(q ∨~r) ∧(~qV~s)∧(~rV~s)∧(qV~s)))∧(~pV~qV~s)

If we choose p to be true, that is p=1, and q to be false, that is q=0, then

(p V((q) ∧(q ∨~r) ∧(~qV~s)∧(~rV~s)∧(qV~s)))∧(~pV~qV~s)

equals 1 as p=1.

Also, (~pV~qV~s) equals 1 as q=0 gives ~q=1.

Thus, we shall get the truth-value of the given proposition to be for p=1 , q=0 and and r and s may take either value 0 or 1

Thus, the given proposition is satisfiable.