CSE 311: Section 0

Task 1 – Warm Up

Translate these English statements into propositional logic, making the atomic propositions as simple as possible and exposing as much of the logic via symbols as possible.

1. “If I am lifting weights this afternoon, then I do a warm-up exercise.”

2. “I can go home only if I have finished my homework.”

Task 2 – More Translations

Translate these English statements into propositional logic, making the atomic propositions as simple as possible and exposing as much of the logic via symbols as possible.

1. “If a red apple falls on my head and I come up with the concept of gravity, then I am Isaac Newton.”

2. “If I find an apple on my doorstep, then I will be very happy, but I will not dance. But if I find an orange on my doorstep, then I will be very happy and I will dance.”

3. “If it is the case that whenever I find lemons, I make lemonade, then it is also the case that whenever I find green apples, I make apple juice.”

Task 3 – English Translations

Translate these propositional logic statements back into English. The atomic propositional logic variables are defined as follows:
$a$: The cat sees the mouse.
$b$: The mouse sees the cat.
$c$: The cat catches the mouse.
$d$: The mouse is scared.
$e$: The cat chases the mouse.
$f$: The mouse stands still.

1. $(a \land \lnot b) \rightarrow (\lnot d \land c)$

2. $(a \land b) \rightarrow (((f \rightarrow (d \land c)) \land (\lnot f \rightarrow (e \land \lnot c)))$

Task 4 – The Calm Before the Form

Consider the boolean functions $F(A, B, C)$ and $G(A, B, C)$ specified by the following truth table:

1. Write the DNF and CNF expressions for $F(A, B, C)$.

2. Write the DNF and CNF expressions for $G(A, B, C)$.

Task 5 – Circuits

Translate the following circuit into a logical expression.