.Open Discrete Math Assignment #2 Evens Solution - 6:30PM

. Introduction

Below is the solutions to the even problems for assignment #2...

1.2:
42:

.Image 1_2_42.png Missing Picture!

1.3 
2:

.Table p    p'    (p')'
.Row T    F    F' = T
.Row F    T    T' = F
.Close.Table

4a:

.Table p    q    r    (p or q) or r    p or (q or r)
.Row T    T    T    (T or T) or T = T    T or (T or T) = T
.Row T    T    F    (T or T) or F = T    T or (T or F) = T
.Row T    F    T    (T or F) or T = T    T or (F or T) = T
.Row T    F    F    (T or F) or F = T    T or (F or F) = T
.Row F    T    T    (F or T) or T = T    F or (T or T) = T
.Row F    T    F    (F or T) or F = T    F or (T or F) = T
.Row F    F    T    (F or F) or T = T    F or (F or T) = T
.Row F    F    F    (F or F) or F = F    F or (F or F) = F
.Close.Table

4b:

.Table p    q    r    (p and q) and r    p and (q and r)
.Row T    T    T    (T and T) and T = T    T and (T and T) = T
.Row T    T    F    (T and T) and F = F    T and (T and F) = F
.Row T    F    T    (T and F) and T = F    T and (F and T) = F
.Row T    F    F    (T and F) and F = F    T and (F and F) = F
.Row F    T    T    (F and T) and T = F    F and (T and T) = F
.Row F    T    F    (F and T) and F = F    F and (T and F) = F
.Row F    F    T    (F and F) and T = F    F and (F and T) = F
.Row F    F    F    (F and F) and F = F    F and (F and F) = F
.Close.Table

10a:
.Table p    q    [p' & (p | q)] -> q
.Row T    T    T
.Row T    F    T
.Row F    T    T
.Row F    F    T
.Close.Table

10b: 
.Table p    q    r    [(p -> q) & (q -> r)] -> (p -> r)
.Row T    T    T    T
.Row T    T    F    T
.Row T    F    T    T
.Row T    F    F    T
.Row F    T    T    T
.Row F    T    F    T
.Row F    F    T    T
.Row F    F    F    T
.Close.Table

10c: 
.Table p    q    [p & (p -> q)] -> q
.Row T    T    T
.Row T    F    T
.Row F    T    T
.Row F    F    T
.Close.Table

10d: 
.Table p    q    r    [(p | q) & (p -> r) & (q -> r)] -> r
.Row T    T    T    T
.Row T    T    F    T
.Row T    F    T    T
.Row T    F    F    T
.Row F    T    T    T
.Row F    T    F    T
.Row F    F    T    T
.Row F    F    F    T
.Close.Table

1.4:

2a. True
2b. False
2c. False
2d. True

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.Close Discrete Math Assignment #2 Evens Solution - 6:30PM