Relations

Question 1

Nothing causes everything.

Answer 1

~(∃x)(y)Cxy

Question 2

Nothing causes anything.

Answer 2

(x)(y)~Cxy

Question 3

Something causes everything.

Answer 3

(∃x)(y)Cxy

Question 4

Everyone is obligated to someone.

Answer 4

(x)(Px→(∃y)(Py∙Oxy))

Question 5

Everything is caused by something (or other).

Answer 5

(x)(∃y)Cxy

Question 6

Some philosopher studies every book with some teacher.

Answer 6

(∃x)[Px∙(y)(By→(∃z)(Tz∙Sxyz))]

Question 7

Every philosopher studies some book with every teacher.

Answer 7

(x)(Px→(∃y)(By∙(z)(Tz→Sxyz)))

Question 8

No philosopher studies any book with any teacher.

Answer 8

~(∃x)(Px∙(∃y)(By∙(∃z)(Tz∙Sxyz)))

Question 9

No one is obligated to everyone.

Answer 9

~(∃x)(Px∙(y)(Py→Oxy))

Question 10

Some number is greater than itself.

Answer 10

(∃x)(Nx∙Gxx)

Question 11

Everything is either colorless or the same color as itself.

Answer 11

(x)(~Cx∨Sxx)

Question 12

No logician argues about every subject with everyone.

Answer 12

~(∃x)(Lx∙(y)(Sy→(z)(Pz→Axyz)))

Question 13

No one laughs at anyone.

Answer 13

(x)(Px→~(∃y)(Py∙Lxy))