Dmath

2.1 Write Mathematical Expressions

Write the following formulas using the Markdown equation editing feature (LaTeX / Mathematics).

#	text	formula
1	IF (P AND Q) THEN R	$(P \wedge Q) \rightarrow R$
2	(P XOR Q) OR R	$(P \oplus Q) \vee R$
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	$P \rightarrow Q \equiv \neg P \vee Q$
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 Translate Sentences into Logic Formulas

Using the propositions:

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

Translations:

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

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

3. The professor does not accept bribes, but I study and will pass the course. Formula: $\neg r \wedge (p \wedge q)$

4. If I study, the professor will accept bribes and I will pass the course. Formula: $p \rightarrow (r \wedge q)$

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