Hint for Section 1.3 Question 1b: Truth table approach

1b) Let c represent "Bill is a cheater",  and let s represent "Bill sits in the back row." Now write each of the premises and the conclusion in symbolic form.

The first premise (p₁) is "If Bill is a cheater, then Bill sits in the back row." This can be written symbolically as  c s.
The second premise (p₂) is "Bill sits in the back row." This can be written symbolically as  s.
The conclusion (q) is "Therefore Bill is a cheater." 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 s) L (s)] c.

Now construct a truth table.

c	s		c s	s		c

Complete the four different truth value combinations for the variables c and s. Then complete the other columns of the truth table.

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