# Few propositional logic questions

• Panphobia
In summary: It is just if p then q.right, because "knowing the right people" is not the only way to get electedso "if p then q" works but "if q then p" doesn'thence, not an "iff" statementIn summary, the given propositions are not clearly defined and thus cannot be determined as true or false. For the propositional expression involving two propositions p and q, the correct phrasing would be "if p then q".
Panphobia

## Homework Statement

Are these propositions, if so are they true or no?

a. $\sqrt{n}$ = 2

b. Consider an integer n: $\sqrt{n}$ = 2 and n = 4

c. Consider an integer n: if $\sqrt{n}$ = 2 then n = 4

Here is another question.

Translate the following into a propositional expression involving two propositions p and q.

d. Philip gets caught whenever he cheats.

## The Attempt at a Solution

a. I would this this is a proposition and it is false because we don't know what n is defined as.
b. Proposition and false because we don't know what n is defined as.
c. Proposition and true because FALSE → FALSE = TRUE

d. p = Philip gets caught
q = he cheats
I am not sure if this is an, if and only if, or just an if then.

A proposition is something you can rephrase as "IF something THEN something else"

sometimes is not very explicit, sometimes is quite obvious

however be careful with saying FALSE just because so and so is not defined.
for example: in b the statement itself is defining n:
n is the number whose square roott is 2

Last edited:
Yes but sometimes wasn't in any of these. I am thinking it is, if p then q, more because Philip getting caught is not contingent on him cheating, he could be caught doing something else.

Panphobia said:
he could be caught doing something else.

Sure.

but whenever he cheats he undoubtly gets caught.

do not confuse "if he cheats then he gets caught" (he's bad at hiding it or something)
with
"if he gets caught then he was cheating" (he can get away with anything except cheating)

these two are completely different statements

So the answer is, if he cheats then he gets caught

yup!

1 person
Another one is pretty confusing also, "Getting elected follows from knowing the right people". So if p = getting elected and q = knowing the right people, so if p then q works, but p iff q also works, if q then p doesn't work. Is it p iff q or if p then q?

this one is phrased confusingly indeed

but remember:
in order to "iff" to work:

BOTH "if p then q" AND "if q then p" have to work

## 1. What is propositional logic?

Propositional logic, also known as sentential logic, is a branch of logic that deals with logical relationships and properties of statements, also referred to as propositions. It is concerned with the logical structure and validity of arguments based on these propositions.

## 2. What are some examples of propositions?

Propositions are statements that can be either true or false. Some examples include "The sky is blue," "All cats have tails," and "2+2=4." These statements can be evaluated as either true or false based on the evidence or reasoning presented.

## 3. How is propositional logic different from other branches of logic?

Propositional logic is different from other branches of logic, such as predicate logic, in that it deals with simple propositions rather than more complex statements involving variables and quantifiers. It is often used as a building block for more complex logical systems.

## 4. What are some common logical operators used in propositional logic?

Some common logical operators used in propositional logic include "and," "or," "not," and "if-then." These operators allow for the combination and manipulation of propositions to form new statements.

## 5. How is propositional logic used in real life?

Propositional logic has many applications in fields such as philosophy, mathematics, computer science, and linguistics. It is often used as a tool for analyzing and evaluating arguments, as well as for constructing complex logical systems and models.

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