In this question, you have to construct formal proofs using the natural deduction rules. The Fitch system

makes use of these rules.

A summary of the rules of natural deduction is given on pages $573$ to $578$ of your textbook. Consult this

when you do question $5.$ Remember that De Morgan$$s laws and other tautologies are not permissible

natural deduction rules. You are also not allowed to use Taut Con, Ana Con, or FO Con. It is important to

number your statements, indicate subproofs, and at each step give the rule that you are using.

Hint: If you have access to a computer, take advantage of the fact and use Fitch.

$6\mathrm{.}1$

Using the natural deduction rules, give a formal proof that the following three sentences are inconsistent:

A $$ B

$$ A

$$ BIn this question, you have to construct formal proofs using the natural deduction rules. The Fitch system

makes use of these rules.

A summary of the rules of natural deduction is given on pages $573$ to $578$ of your textbook. Consult this

when you do question $5.$ Remember that De Morgan$$s laws and other tautologies are not permissible

natural deduction rules. You are also not allowed to use Taut Con, Ana Con, or FO Con. It is important to

number your statements, indicate subproofs, and at each step give the rule that you are using.

Hint: If you have access to a computer, take advantage of the fact and use Fitch.

$6\mathrm{.}1$

Using the natural deduction rules, give a formal proof that the following three sentences are inconsistent:

A $$ B

$$ A

$$ B

$6\mathrm{.}2$

Using the natural deduction rules, give a formal proof of:

SameSize$($b$,$ c$)->($Large$($c$)$ Small$($c$))$

from the premises:

$1.$ Small$($a$)->$ Small$($b$)$

$2.$ Small$($b$)->($SameSize$($b$,$ c$)->$ Small$($c$))$

$3.$Small$($a$)->($Large$($a$)$ Large$($c$))$

$6\mathrm{.}3$ In this question, you have to construct formal proofs using the natural deduction rules. The Fitch system

makes use of these rules.

A summary of the rules of natural deduction is given on pages $573$ to $578$ of your textbook. Consult this

when you do question $5.$ Remember that De Morgan's laws and other tautologies are not permissible

natural deduction rules. You are also not allowed to use Taut Con, Ana Con, or FO Con. It is important to

number your statements, indicate subproofs, and at each step give the rule that you are using.

Hint: If you have access to a computer, take advantage of the fact and use Fitch.

$6\mathrm{.}1$

Using the natural deduction rules, give a formal proof that the following three sentences are inconsistent:

AvvB

notA

notB

$6\mathrm{.}2$

Using the natural deduction rules, give a formal proof of:

SameSize$($b$,$ c$)$ Large$($c$)vv$ Small$($c$))$

from the premises:

Small$($a$)$ Small$($b$)$

Small$($b$)($SameSize $($b$,$ c$)$ Small$($c$))$

$$ Small$($a$)($Large $($a$){?}^{{?}^{?}}$ Large$($c$)$

Using the natural deduction rules, give a formal proof of $($A $->[$B $->$ C$])([$A $$ B$]->$ C$)$ from no

premises.

$6\mathrm{.}4(14)$

Using the natural deduction rules, give a formal proof of:

A $$B from premises

$1.$ A $$ B $$ C

$2.$ B $->($A $->$C$)$

$3.$ A $$ C