Part (b): Practice and Review Due Friday, January 20, at 10:00 pm
Please prepare long-form answers to each question in this part of the assignment.
$$ \frac{sin\ A}{a} =\frac{sin\ B}{b} = \frac{sin\ C}{c} $$
<aside> 💡 (a) is a proposition, but I can't determine if it's true because I don't have accurate data on Toronto's population.
(b) is not a proposition, because there is no limit to the meaning of “$A,B,C,a,b,c$ ” to determine the true or false.
(c) is not a proposition, because it is a Liar paradox arising from self-reference.
$$
\text{If we determin the statement r is true, then The statement}\\ r\\ \\text{is false." is true,}\\\\ \\text{Then we get the statement r (The statement r is false") is true。}
$$
</aside>
<aside> 💡 (a) 3 atomic propositional variables $(p,q,r)$
(b) $2^3=8$ rows
(c) $(p\vee q),(p\rarr r)\ and (q\rarr r)$ these 3 columns are required.
(d) & (e) $(p\vee q)\rarr r$ and $(p\rarr r)\wedge (q\rarr r)$ this 2 columns are identical:
| $p$ | $q$ | $r$ | $p\vee q$ | $p\rarr r$ | $q\rarr r$ | $(p\vee q)\rarr r$ | $(p\rarr r)\wedge (q\rarr r)$ |
|---|---|---|---|---|---|---|---|
| T | T | T | T | T | T | T | T |
| T | T | F | T | F | F | F | F |
| T | F | T | T | T | T | T | T |
| T | F | F | T | F | T | F | F |
| F | T | T | T | T | T | T | T |
| F | T | F | T | T | F | F | F |
| F | F | T | F | T | T | T | T |
| F | F | F | F | T | T | T | T |
| </aside> |
<aside> 💡 (a).I think it should be inclusive because John can be a mathematician and an NFL player in the same time.
</aside>
(b). ( i )