_> CSCI 2610E - Homework 1
__ <!> Instructions
> |> Type your answers in a \graf file and submit the file to eLC.
> |> Check your document *{before} submitting it to eLC. Then *{verify} that your file uploaded successfully.
> |> Your \graf code must compile and render in order to receive credit.
> |> Homework is not a group assignment. You may study with people but do your own work and write up your own solutions.
__ @{task} Exercises
(1) For each of the following @prptns, construct an @eqnt @prptn that uses !{only the 3 native operators} (AND, OR, and NOT).
> [a] p \!^ (q (+) r)
> [b] p <- (q (+) r)
> [c] (p \!v q) -> \!(p \^ q)
\;
(2) Use the logical identities to prove that
>< p<->q==\!(p(+)q).
Annotate each line with the name of the identity used in that line. You must cite each identity used in order to get full credit.
\;
(3) Use the logical identities to prove that
>< (p->r)\v(q->r) == (p\^q)->r.
Annotate each line with the name of the identity used in that line. You must cite each identity used in order to get full credit.
\;
(4) Use the logical identities to prove that the proposition
>< \!(p->q) -> \!q
is a tautology. Annotate each line with the name of the identity used in that line. You must cite each identity used in order to get full credit.
\;
(5) Let p, q, and r be the following propositions:
> p: It is raining.
> q: Max walks to class.
> r: Max misses class.
\;
Give English translations of the following statements:
a) p -> \!q
b) q -> \!r
c) (p \^ \!r) -> q
d) \!q \v \!p
e) r \v q