Answer:
The conclusion "T" logically follows from the premises given and the argument is valid
Step-by-step explanation:
Let us use notations to represent the steps
P: I take a bus
Q: I take the subway
R: I will be late for my appointment
S: I take a taxi
T: I will be broke
The given statement in symbolic form can be written as,
(P V Q) → R
S → (¬R ∧ T)
(¬Q ∧ ¬P) → S
¬R
___________________
∴ T
PROOF:
1. (¬Q ∧ ¬P) → S Premise
2. S → (¬R ∧ T) Premise
3. (¬Q ∧ ¬P) → (¬R ∧ T) (1), (2), Chain Rule
4. ¬(P ∨ Q) → (¬R ∧ T) (3), DeMorgan's law
5. (P ∨ Q) → R Premise
6. ¬R Premise
7. ¬(P ∨ Q) (5), (6), Modus Tollen's rule
8. ¬R ∧ T (4), (7), Modus Ponen's rule
9. T (8), Rule of Conjunction
Therefore the conclusion "T" logically follows from the given premises and the argument is valid.
You sometimes need to rewrite a factor because the lead number is not between 1 and 10 as it needs to be in scientific notation. For instance, if we had lead numbers of 2 and 5, as we do in the following problem.
2x10^3 * 5x10^9
Then we get the answer of 10x10^12. We need to adjust this by moving the decimal place and increasing the exponent by 1. The correct answer would be 1x10^13 instead.
Answer:
£18
Step-by-step explanation:
Let
x = original price of the game
Increase in price = 1/2
New price = £27
x + 1/2x = £27
2x+x/2 = 27
3/2x = 27
x = 27 ÷ 3/2
= 27 × 2/3
= 54 / 3
x = £18
Therefore, the original price of the game is £18
I'm not completely sure but this is what I would do.
evaluate <span>(1/ 4)^x - 1 </span>as is. But change the (1 /2)^2x to (2/4)^2x. This way both fractions have the same denominator and in this sense, the same base. The 2/4 base still evaluates into 1/2 so nothing, mathematically, is being broken here.
