4 1/4 + (-1 3/4) what is the answer

Mathematics

1 answer:

aliya0001 [1]3 years ago

7 0

Answer:

2.5 or 250.

Step-by-step explanation:

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Determine which, if any, of the three statements are equivalent.

patriot [66]

Answer:

Statement (b) is equivalent to statement (c), but neither is equivalent to statement (a).

Step-by-step explanation:

Let $F$ denote that "Fido is our fish's name" and let $R$ denote that "Rex is our dog's name". The statements listed in this question would then become:

(a) $F \implies R$ ;
$F$ implies $R$ .
(b) $\lnot ((\lnot F) \land (\lnot R))$ ;
not ((not $F$ ) or (not $R$ )).
(c) $F \lor R$ ;
$F$ or $R$ .

Apply de Morgan's Law $\lnot (P \land Q) \iff (\lnot P) \lor (\lnot Q)$ to rewrite statement (b). Let $P = (\lnot F)$ and $Q = (\lnot R)$ . By de Morgan's Law:

$\begin{aligned} & \lnot ((\lnot F) \land (\lnot R)) \\ \iff \; & \lnot (P \land Q)\\ \iff \; & (\lnot P) \lor (\lnot Q) && (\text{by de Morgan's Law}) \\ \iff \; & (\lnot (\lnot F)) \lor (\lnot (\lnot R)) \\ \iff \; & F \lor R\end{aligned}$ .

In other words, statement (b) $\lnot ((\lnot F) \land (\lnot R))$ is equivalent to statement (c) $F \lor R$ .

Statement (a) $F \implies R$ isn't equivalent to $F \lor R$ .

For example, when $F = \texttt{True}$ and $R = \texttt{False}$ , $F \implies R$ would be false since $\texttt{True}$ does not imply $\texttt{False}$ . However, for the same $F$ and $R$ , $F \lor R$ would be true since $F = \texttt{True}\!$ .