Hint for Section 1.3 Question 1c: Truth table approach

1c) Let c represent "the cat fiddled", let j represent "the cow jumped over the moon", let d represent "the little dog laughed", and let r represent "the dish ran away with the spoon." Now write each of the premises and the conclusion in symbolic form.

The first premise (p1) is "If the cat fiddled or the cow jumped over the moon, then the little dog laughed." This can be written symbolically as  (c V j) impliesred.jpg (864 bytes) d.
The second premise (p2) is "If the little dog laughed, then the dish ran away with the spoon." This can be written symbolically as  d impliesred.jpg (864 bytes) r.
The third premise (p3) is "But the dish did not run away with the spoon." This can be written symbolically as ~r.
The conclusion (q) is "Therefore the cat did not fiddle." This can be written symbolically as  ~c.

Remember that an argument is written as a conjunction of the premises implies the conclusion. So this argument can be represented as
[(c V j) impliesred.jpg (864 bytes) d) L (d impliesred.jpg (864 bytes) r) L (~r)] impliesred.jpg (864 bytes) (~c).

Now construct a truth table.

c j d r   (c V j) implies.jpg (563 bytes) d d implies.jpg (563 bytes) r ~r   ~c
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   

Complete the sixteen different truth value combinations for the variables c, j, d and r. Then complete the other columns of the truth table.

Next hint please
Back to Section 1.3
Full solution