Let T: P_3 rightarrow P_3 be the linear transformation satisfying T(1) = 2x^2 -4, T(x) = 2x + 9, T(x^2) = -5x^2 + x - 7. Find the image of an arbitrary quadratic polynomial ax2^ + bx + c. T(ax^2 +bx + c) =. Solution T(ax² + bx + c) = aT(x²) + bT(x) + cT(1) =a(-5x^2 +x-7) +b(2x+9) +c(2x^2 -4) =(-5a+2c)x^2 +x(a+2b)+(-7a +9b -4c).

1. Linguistics
Exercise 1. For each pair of sentences X and Y below, say whether or not X entails Y. If it
doesn't, give an example of a situation where X is true but Y is not.
a. X: Fifi is a poodle. Y: Fifi is a dog.
b. X: My last name is Jones. Y: My father's last name was Jones.
c. X: I live in Ohio. Y: I live in the U.S.A.
d. X: I speak Russian. Y: I am from Russia.
e. X: At least 30 people will come to the party. Y: At least 20 people will come to the party.
f. X: If you go to the party, I'll go too. Y: If you don't go to the party, I won't go.
Solution
a) true
b)true
c)Ohio
d) true
e)true
f)true