My Discrete Math Repository

Homework 2 - 202255624 현승민

2.1 Equation Editing

#	text	formula
1	IF (P AND Q) THEN R	$(P \land Q) \to R$
2	(P XOR Q) OR R	$(P \oplus Q) \lor R$
3	NOT P IFF Q	$\neg P \leftrightarrow Q$
4	FOR ALL x, P(x)	$(\forall x)P(x)$
5	THERE EXISTS AN x, NOT Q(x)	$(\exists x)\neg Q(x)$
6	IF P THEN Q EQUIVALENT TO NOT P OR Q	$P \to Q \equiv \neg P \lor Q$
7	Euler's Identity	$e^{i\pi} + 1 = 0$
8	SUM of n from 1 to 100 Equals 5050	$\sum_{n=1}^{100} n = 5050$

2.2 Translation

Using the propositions

• $p$ = "I study"
• $q$ = "I will pass the course"
• $r$ = "The professor accepts bribes"

Translate the following into statements of propositional logic:

1. If I do not study, then I will only pass the course if the professor accepts bribes.
   $\neg p \to (q \to r)$

2. If the professor accepts bribes, then I do not study.
   $r \to \neg p$

3. The professor does not accept bribes, but I study and will pass the course.
   $\neg r \land p \land q$

4. If I study, the professor will accept bribes and I will pass the course.
   $p \to (r \land q)$

5. I will not pass the course but the professor accepts bribes.
   $\neg q \land r$