Let p be: John goes to the beach
Let q be: He will go surfing.
Then in symbolic form, the argument becomes:
p ⇒ q
p
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∴ q
An argument is valid if the conjuction of the premises implies the conclusion.
p | q | p ⇒ q | (p ⇒ q) ∧ p | [(p ⇒ q) ∧ p] ⇒ q
---------------------------------------------------------------------\
F | F | T | F | T
F | T | T | F | T
T | F | F | F | T
T | T | T | T | T
The table above shows that the argument is a tautology.
Hence, the argument is valid
Functions can be modeled by equations, tables and graphs
From the question, we have the following ordered pairs
(x,y) = (0,1) and (4,2)
The function is a linear function.
So, we start by calculating the slope (m) using:
Substitute known values
The equation is then calculated as:
This gives
The domain of the above function is the set of whole numbers
Substitute 10 for x, to calculate the number of box office gross for week 10
Approximate
Hence, the company should expect 4 box office gross in week 10
Read more about linear functions at: