What is an argument? What is a tautology?

Provide an example of modus ponens using real world statements, or premises.

What are some scenarios in which you have used arguments that meet the definition you’ve stated here?

Here is my classmates answers that you must write an answer to.

What is an argument? What is a tautology?

An argument is a sequence of statements that end with a conclusion.

A tautology is a compound proposition that is always true, regardless what the truth values of the propositional variables are.

Provide an example of modus ponens using real world statements, or premises.

“If the Royals win 4 out of 7 World Series games, then they are World Series champions.”

“The Royals won 4 out of 7 World Series games.”

——————————————————————————————————-

THEREFORE “The Royals are World Series champsions.”

What are some scenarios in which you have used arguments that meet the definition you’ve stated here?

Modus ponens can be seen frequently throughout the day all over the world as it is more or less an argument of common sense. For instance, if you buy a lottery ticket in hopes of (obviously) winning the lottery:

“If the lottery drawing draws 1 2 3 4 5 6, you win the lottery.”

“The lottery drew 1 2 3 4 5 6.”

———————————————————————–

THEREFORE “You win the lottery.”

Here is the second classmate.

An argument is a series of premises that if all true prove a conclusion. A tautology is when the combination of propositions is always true no matter what truth values the propositions have. For example, the rule of inference called modus ponens is based on the tautology that ( p^(p->q))->q. A real life example of modus ponens would be as follows:

If it is cold outside, then I will wear a coat.

It is cold outside.

Therefore,

I will wear a coat.

qed

Changing our propositions into propositional variables we will let p represent “it is cold outside” and let q represent “It is cold outside.”

Now, the argument has the form:

p->q

p

Therefore, q

qed

I use the aforementioned argument very frequently as the weather is beginning to change in my region.

Another example would be in establishing expectations for employees at work as follows:

If you master your current position, then you begin training on another position.

You master your current position.

Therefore, you begin training on another position.

qed

I can think of countless examples where this form of argumentation is used. For instance, in proof of solving an algebraic equation for x,

if x plus 12 equals 17, x equals 5

x plus 12 equals 17

Therefore, x equals 5

qed