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# Section # 1 Determine the truth value of the given statement. Assume that A, B, C, or D are true and X, Y, Z are false.

**Section # 1 **

Determine the truth value of the given statement. Assume that A, B, C, or D are true and X, Y, Z are false. Complete the entire statement by placing all values in for the given letters. __Circle your__ __answer__. Show all of your work for full credit.

1. ~ { [ (~ C v ~ D) • (Z v ~ A ) ] É ~ [ ~ (D v ~Y ) v ( X v ~ Z ) ] }

2. {[ A É ( B É C ) ] É [ ( A • B ) É C ]} É [ ( Y É B ) É ~ ( C É ~ Z ) ]

3. ~ {~ [ (Y v ~ Z) • (A v ~ X ) ] • ~ [~ (Y v A) • (~ C v B ) ]}

**Section # 2**

If A, B, are true, and X, Y, are false, and P, Q are unknown, determine the truth value of the following. Fully complete each equation. If the truth value of the statement cannot be determined, write "undetermined." __Circle your answer__. Show all of your work for full credit.

1. B É ~ P

2. [ Q v ( B · Y ) ] É [ ( Q v B ) · ( Q v ~ Y ) ]

3. ( P É X) É { [ P É ( X É Q ) ] É ( P É Q ) }

**Section # 3**

Determine whether the following arguments are either valid or invalid by using **truth tables only**. __Write out your answer next to the problem and also circle your proof (i.e. show which line(s) are invalid) . __Show all of your work for full credit.

1. ( O v P ) É Q / Q É ( O • P ) // ( ~ O v P ) É ( ~ O • P )

2. (Q v S ) É ( ~ P · P ) / ~ Q v S // ~ Q É ( S v P )

3. W É X / X É W / ~X É ~ Y / Y • X // W º ~Y

4. Z // E É ( Z É E )

**Section # 4 **

Determine whether the following arguments are either valid or invalid by using the indirect method __only__ of establishing validity. __Circle your answer__. Show all of your work for full credit.

1. G É ( I v D ) / ( I • D ) É B // G É B

2. ( ~ J · ~ K ) / ( L É J ) / ( M É K ) / ( M É ~ L ) É ~ ( N · O ) // ~ N

3. ~ ( O • Z ) É ( M • ~ A ) / M É R / Z ≡ ~ O / ~ R v A // ~ O ≡ ~ R

4. ( Z • K ) v ~ ( R É O ) / ( O v M ) É ~ R / ( M • K ) ≡ R // ~ Z ≡ O

5. ( A É B ) É ( C • D) / (~ A v ~ B ) É E / ~E // (~ C • ~ D ) É E

6. B É ( E · D ) / ( ~ E v ~ F ) / E É ( B v G ) / G É ( D É F ) // G v ~ E

**EXTRA CREDIT: 5 POINTS! **

**LET'S TEST THOSE ANALYTICAL SKILLS!**

**Extra Credit:**

Around a campfire are seated four (4) marries couples: Bob and Connie, Dan and Ellen, Gary and Holly, and Jack and Karen. All eight people are equally spaced around the campfire.

Additional info:

No husband sits next to his wife.

Bob is seated next to Karen.

Dan and Ellen sit directly across from each other.

Connie is seated next to Holly.

1. Which following pairs of people may sit next to each other?

A. Connie and Karen

B. Holly and Bob

C. Gary and Jack

D. Ellen and Holly

E. Karen and Jack

2. If Connie sits directly across from Bob and next tot Ellen, which of the following people must sit next to Gary?

A. Dan

B. Karen

C. Jack

D. Bob

E. Connie