Introduction to Logic - Exercise 6.1

Introduction to Logic

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Exercise 6.1 - Clausal Form

For each of the following sentences, say which set of clauses is the correct clausal form.

1.	p ∧ q ⇒ r ∨ s
	{p, q, r, s}
	{¬p, ¬q, r, s}
	{¬p, ¬q, r}, {¬p, ¬q, s}
	{¬p, r, s}, {¬q, r, s}
	{¬p}, {¬q}, {r}, {s}

2.	p ∨ q ⇒ r ∨ s
	{p, q, r, s}
	{¬p, ¬q, r, s}
	{¬p, ¬q, r}, {¬p, ¬q, s}
	{¬p, r, s}, {¬q, r, s}
	{¬p}, {¬q}, {r}, {s}

3.	¬(p ∨ q ∨ r)
	{¬p, ¬q, ¬r}
	{¬p}, {¬q}, {¬r}

4.	¬(p ∧ q ∧ r)
	{¬p, ¬q, ¬r}
	{¬p}, {¬q}, {¬r}

5.	p ∧ q ⇔ r
	{p, q}, {r}
	{¬p, ¬q}, {r}
	{¬p, ¬q, r}, {¬r, p}, {¬r, q}
	{¬p, r}, {¬q, r}, {p, q, ¬r}
	{p}, {q}, {r}