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3 years ago

Describe the transformation from f(x)=x for m(x)=(x-5) Ask for details

Mathematics

1 answer:

Likurg_2 [28]3 years ago

5 0

Answer:

m(x)=f(x)-5

the line formed by f(x) when transformed into m(x) shifts down 5 units on the (x,y)-plane

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I need the correct answer for questions 1

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The truth values of the propositions are false, true and false

<h3>How to determine the true values?</h3>

The Boolean variables are given as:

p = false

r = false

q = true

s = true

The truth values of the propositions are as follows:

As a general rule:

∧ means and

¬ not

∨ or

So, we have:

(true → (false ∧ ¬ false)) ∧ ((false → (false ∨ true)) ∧ true)

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So, we have:

(true → (false ∧ true)) ∧ ((false → (false ∨ true)) ∧ true)

false ∧ true = false and false ∨ true = true

So, we have:

(true → false) ∧ ((false → true) ∧ true)

false → true = true and true → false = false

So, we have:

(false) ∧ (true ∧ true)

true ∧ true = true

So, we have:

false ∧ true

Lastly

false ∧ true = false

Hence, the truth value of (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s) is false

This means

((false ∧ ¬ true) → (true ∧ false)) → (true ∨ ¬true)

Using the established rules in (1), we have:

((false ∧ false) → (true ∧ false)) → (true ∨ false)

This gives

((false → false)) → true

This gives

true → true

Lastly, we have:

true

Hence, the truth value of ((false ∧ ¬ true) → (true ∧ false)) → (true ∨ ¬true) is true

This gives

(false → true) ∧ (true → false)

Using the established rules in (1), we have:

true ∧ false

This gives

false

Hence, the truth value of (p → q) ∧ (q → r) is false