Give English language translations of the following wffs if M(x): x is a man
W(x): x is a woman

I: Ivan
P: Peter
W(x, y): x works for y

a. (∃x)(W(x) Λ (∀y)(M(y) → [W(x, y)]’))
b. (∀x)[M(x) →(∀y)(W(x, y) → W(y))]
c. (∀x) (∀y)(M(x) ΛW(y, x) →W(y))
d. (∀x)[M(x) →(∃y)(W(y) Λ W(x, y))]
e. (∀x)[W(x, i) → (W(x))’]

b

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

shorter then the tree