7.3i
The Problems and answers for Mock Exam 2, part XIII

The rules are here. ALL ANSWERS ARE AT THE BOTTOM OF THIS PAGE.



Justification:       Sentence:       

Problem One.  

Premise

1

(^x)(Wx>Mx)

1 ^E

2

Wh>Mh

Problem Two.  

Premise

1

Ws

Premise

2

Hs

1,2 &I

3

Ws&Hs

3 %I

4

(%x)(Wx&Hx)

Problem Three.  

Premise

1

(%x)(Wx&Hx)

1 CM

2

(%x)(Hx&Wx)

Problem Four.  

Premise

1

(^x)(Wx>Mx)

Premise

2

(^x)(Wx>Hx)

Premise

3

Ws

1 ^E

4

Ws>Ms

3,4 MP

5

Ms

2 ^E

6

Ws>Hs

3,6 MP

7

Hs

5,7 &I

8

Hs&Ms

8 %I

9

(%x)(Hx&Mx)

Problem Five.  

Premise

1

(^x)(Ax=Tx)

1 ^E

2

Ar=Tr

2 EQ

3

(Ar>Tr)&(Tr>Ar)

3 &E

4

Tr>Ar

4 ^I

5

(^x)(Tx>Ax)

Problem Six.  

Premise

1

~(^x)(Ax v Bx)

1 QN

2

(%x)~(Ax v Bx)

2 DM

3

(%x)(~Ax&~Bx)

Problem Seven.  

Premise

1

(^x)(Ax v Bx)

 

Premise

2

(%x)~Ax

 

Assumption

3

....what if

~(%x)Bx

3 QN

4

....then...

(^x)~Bx

1 ^E

5

....then...

Ar v Br

4 ^E

6

....then...

~Br

5,6 DS

7

....then...

Ar

7 ^I

8

....then...

(^x)Ax

2 QN

9

....then...

~(^x)Ax

3-9RD

10

(%x)Bx