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.
Now construct a truth table.
| 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. Identify these rows. An argument is valid if the conclusion is true in all the critical rows.