“If you get hired for the job and work hard at it then you will either get a nic

ID: 3677650 • Letter: #

Question

“If you get hired for the job and work hard at it then you will either get a nice bonus or a raise.

If you get the nice bonus you get to go on vacation. However, you did not get to go on vacation.

You get a raise if and only if your boss isn't mean. But your boss is mean. Therefore you must

either not have been hired for the job, or didn't work hard.”

1. Translate the previous passage into SL, capturing as much logical structure as possible. Be sure to write

your translation scheme.

2. Write the column headings you would need to make a truth table to show whether the passage is

deductively valid. (Do not fill-in any truth-values).

3. How many rows would be required? (Don’t actually write the truth-values for any propositions). Explain

how you know.

4. Show that the passage is a deductively valid argument by providing a logical derivation.

Explanation / Answer

SL :

if you get job and workhard , you get bonus or raise.

if it is bonus, vacation or no vacation

raise iff boss isn’t mean

boss is mean

There fore ,you are not hired or didn’t work hard

job = j

workhard = w

bonus = b

raise = r

vacation = v

boss isn’t mean = m

Logical Expression:

j&w = x

b or r = b v r = y

xày

b à v,~v

(r ó m) &~m

Truth table:

j^w=x

b v r= y

x->y

b->v

róm=z

Z^~m=A

~j v ~w=B

A=>B

No.of Rows = 4 by estimation

No.of rows = 9 if you want to use 8 truth values