rite two arguments in English, one in the form of modus ponens and one in the form of modus tollens. Then, write the arguments in symbols using sentence letters and truth-functional connectives. (If your computer does not have all the symbols needed, use some other symbol you do have access to and explain what its meaning is.)

Sure! First, let me explain what Modus Ponens and Modus Tollens are.

Modus Ponens is a valid rule of inference in logic that allows you to infer a conclusion from a conditional statement (also known as an if-then statement) and the affirmation of its antecedent (the "if" part). It can be expressed in the following form:

Argument form:
1. If P, then Q.
2. P.
3. Therefore, Q.

Symbolic representation:
1. P → Q
2. P
3. Q

Now, let's illustrate it with an argument statement in English before representing it symbolically.

English argument (Modus Ponens):
1. If it rains, the ground gets wet.
2. It is raining.
3. Therefore, the ground is wet.

Symbolic representation:
1. R → G
2. R
3. G

On the other hand, Modus Tollens is another valid logical rule of inference that allows you to infer a conclusion from a conditional statement and the negation of its consequent (the "then" part). It can be expressed in the following form:

Argument form:
1. If P, then Q.
2. Not Q.
3. Therefore, not P.

Symbolic representation:
1. P → Q
2. ¬Q
3. ¬P

Now, let's provide an example of an argument in English using Modus Tollens and then represent it symbolically.

English argument (Modus Tollens):
1. If the battery is dead, the car won't start.
2. The car is starting.
3. Therefore, the battery is not dead.

Symbolic representation:
1. B → ¬S
2. S
3. ¬B

In both cases, "->" represents the conditional "if-then" implication, "¬" represents negation (not), "P" and "Q" are sentence letters representing propositions, and the numbering indicates the order of the argument's statements.