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Mathematics

1 answer:

inysia [295]2 years ago

6 0

Answer:

I had to repost my answer because i got deleted from some reason

Step-by-step explanation:

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A businessman bought a personal computer for $10,768. Calculate the selling price of the personal computer if he made a profit o

Maksim231197 [3]

Answer:

$12,060

Step-by-step explanation:

LET selling price be rep by x

since he made a profit of 12%, we then add to 100%

100% + 12% = 112%.

to find the selling price, we multiply cost price by 112%

112% x $10768 =

112 / 100 x $10,768

= 1.12 x $10,768 = 12,060

selling price = $12,060.

5 0

2 years ago

Read 2 more answers

Suppose you want to prove a theorem of the form p → (q ∨ r). Prove that this is equivalent to showing that (p ∧ ¬q) → r.

tino4ka555 [31]

You "distributed" the negation inside the parenthesis. Let's focus on the $\lnot (p\wedge \lnot q)$ part.

We can distribute the negation inside the parenthesis by negating every term, and switching and with or, and vice versa. So, you have

$\lnot (p\wedge \lnot q) \equiv (\lnot p) (\lnot \wedge) (\lnot \lnot q)$

Of course, writing $\lnot \wedge$ is improper, I was just stressing the fact that we distributed the negation to every term in the parenthesis. So, since a double negation cancels out, you're left with

$\lnot (p\wedge \lnot q) \equiv \lnot p \lor q$

which of course implies that

$\lnot (p\wedge \lnot q) \lor q \equiv (\lnot p \lor q) \lor q$

Edit: I actually derived the expression in the opposite order, but since they are equivalent, it doesn't really matters where you start from and where you get to. Anyway, if you actually want to derive $\lnot (p \wedge \lnot q) \lor r$ from $(\lnot p \lor q)$ , you simply have to negate the first parenthesis and distribute the negation as discussed.