Answer
A student from ITECH7410 is smart
Students from ITECH7410 are smart
Explanation
There exists means some one is there
For all means every student
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What does it mean by the following predicate logics: a. 3x. Student(x, ITECH7410) A smart(x) b....
3. In the domain of all movies, let D(x) be the predicate "x has a demon in it." and P(x) be the predicate "x is about ponies." Which one of the following statements represents "Some movies that have a demon in it are not about ponies." (3 points] a. (3x)(D(x) → P(x)) b. (3x)(D(x) A-P(x)) c. (Vx)(P(x) →D(x)) d. (3x)(PD(x)) +-P(x))
Use the rules of deduction in the Predicate Calculus (but avoiding derived rules) to find formal proofs for the following sequents: (a) x) F)~(Vx)~ F(x) (b) (Vz) ~ F(x) B) F() (3x)(G(z) Л (Vy) (F(y) H(y, z))) (e)
Use the rules of deduction in the Predicate Calculus (but avoiding derived rules) to find formal proofs for the following sequents: (a) x) F)~(Vx)~ F(x) (b) (Vz) ~ F(x) B) F() (3x)(G(z) Л (Vy) (F(y) H(y, z))) (e)
(b) (i) Given the function f(x,y)= xe' + 3x, find two unit vectors who are orthogonal to the gradient of f at the point P(3,0). (7 Marks) (ii) In which direction does f(x,y)= xey + 3x increase most rapidly at the point P(3,0)? What is the maximum rate of change at that point? (3 Marks)
B3. Newton Cotes Method (student) [33 pts] 3) Use the Newton-Cotes formula f(x)-x) i-0 to estimate the integral -3x -1 with 5 evenly spaced grid points (compare to your reference value). (Hint: Use the method of undetermined coefficients to solve for the A, by substituting in f : i, x, x2, X3, X4 and demanding that the result of the integral be exact) Repeat with 7 and 9 points. Comment on the improvement to yeur approximations. My Report. Your discussion...
please answer both
3. Differentiate the following using the Difference Quotient. a. f(x) 3x b. g(x) 5 cos(x)
3. Differentiate the following using the Difference Quotient. a. f(x) 3x b. g(x) 5 cos(x)
2. Let X have mean 2 and variance 9. (a) What is the mean and variance of 5-3X? (b) What is the mean and variance of (X - 2)/3? (c) What is the mean and variance of (5X - 10)/2?
3) Given the following 3x-16x +14x-49 f (x) x-Sx What is the equation of the vertical asymptotes? a) b) What is the equation of the horizontal asymptote? (x-7)(x -21x+70) (x-5)'x ')= c) f'(x)-0x 7, x = 4.2, x 16.8 Determine all the partition numbers for f' create a sign chart on f' f(4.2) 3.55 (7)=3 and f(16.8) 2.97 d) Use the above information to determine any local maximums or minimums.
3) Given the following 3x-16x +14x-49 f (x) x-Sx What...
it is about the classical logic in the subject of formal method:
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Question 1: Classical Logic [25 marks)
a) Answer the following questions briefly but precisely.
i. State what it means for an argument to be valid in Predicate
Logic. [3 marks
ii. Suppose you use resolution to prove that KB = a. Does this
mean that a is valid? And why? [3 marks
b) Consider the following three English sentences: Sl: If...
Find the following limit or state that it does not exist. lim 3x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A fim 3x = (Simplify your answer.) X-6 B. The limit does not exist.
For the following linear system: 2x--3x +5x2-7x4-0 X-2x+3x-2xs-0 3x3-3 x-x-3x: 0 X:+8 x 9 x3+11 xs-0 (1) Represent this linear system in the form Ax = b. (ii) Explain what the null space of the coefficient matrix A is in terms of the linear system (ii) Find a basis for the null space of A. (iv) Find the rank and nullity of matrix A.