My Discrete Math Repository

Homework 2 - 202255658 KIM JAE SIK

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.
   $$\neg q \land r$$