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.
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.
| c | s | c  s |
s | c | |||
| T | T | T | T | T | * | ||
| T | F | F | F | T | |||
| F | T | T | T | F | * | ||
| F | F | T | F | F |
The critical rows of the truth table are the rows in which all the premises are true. The critical rows are marked with an *. In one of these rows, the conclusion is false. Hence this argument is NOT valid..