Homework Answers
![je al Nan 13) ass] d) all of the above aj Range (F)=B ..-> fis oolo by de finition of oslo Function by every element of B bas](http://img.homeworklib.com/questions/1e9e65e0-c0c1-11ea-ad05-a92be3483459.png?x-oss-process=image/resize,w_560)
all
of the above statements are equivalent definition of surjective or
onto conditions of f.so no need to explain more.
All are definitions of onto function f.
Answer)d)all of the above.
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Question 13 5 pts Which of the following is true for a function f : A...
(d) Given a function X Y show that each of the following statements are equivalent: (D)...
(d) Given a function X Y show that each of the following statements are equivalent: (D) f is surjective (or, onto) (ii) there exists a function Y 4Xsucht hat.ro9주1r M for every pair of functions Y-ltLr/ifper Ctl
Incorrect Question 7 0/5 pts Which of the following proposition is true? (A) The clause {P(a,x,f(g(y))),...
Incorrect Question 7 0/5 pts Which of the following proposition is true? (A) The clause {P(a,x,f(g(y))), P(z,f(z),f(u))} is unifiable and the set MGU = {[z/a], [x/f(a)], [u/g(y)]} is the most general unifier for it. (B) The clause (P(f(a),g(x)), P(7.7)} is not unifiable. (C) The clause {P(a,x), P(z,f(z))} is unifiable and the set MGU {[z/a], [x/f(a)]) is the most general unifier for it. (D) All of the above. (A (B) (C) (D)
The definition we gave for a function is a bit ambiguous. For example, what exactly is a "rule"? ...
The definition we gave for a function is a bit ambiguous. For example, what exactly is a "rule"? We can give a rigorous mathematical definition of a function. Most mathematicians don't use this on an everyday basis, but it is important to know that it exists and see it once in your life. Notice this is very closely related to the idea of the graph of a function. Definition 9. Let X and Y be sets. Let R-X × Y...
Question 13 5 pts Determine whether the function is one to one or not: {(-3,-5) (-2,-4)...
Question 13 5 pts Determine whether the function is one to one or not: {(-3,-5) (-2,-4) (-1, -3) (0, -2)(-1,-1) (-2, 0) (-3, 1)} Yes No, it is not one to one Oo oo Not a function None of the above. 5 pts Question 14 Find the inverse of the function: f (x) = x3 + 13 f'(x) = V2 - 13 y=2-13 33 = 2 - 13 None of the above. Question 15 5 pts Given f (x) =...
Question 13 4 pts Which of the following hydrocarbons has one pi bond and one cycloalkane?...
Question 13 4 pts Which of the following hydrocarbons has one pi bond and one cycloalkane? A) C6H8 B) C5Hg C) C3H8 D) C4H8 OB ОА Ос OD 4 pts
Notice that the following claim is among one of the multiple steps of proving an important result...
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Notice that the following claim is among one of the multiple steps of proving an important result: if A C and B D then A × B C × D. Claim: Let f : A → C and g : B → D be two surjective (onto) functions. Then h: A x B-> C D defined by ћ((a, b))-(f(a), g(b)) is a well-defined function that is surjective. Proof: Since f maps each a E A into f(a)...
A function f : A - B is said to be injective (or one-to-one) provided Va,...
A function f : A - B is said to be injective (or one-to-one) provided Va, a2 € A, f(a) = f(az) ► a1 = . A function g: A + B is said to be surjective (or onto) provided W6 € B, 3 some a € A such that g(a) = b. A function h: A → B is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective. The following...
Is the statement true or not true? and why? "Every function where f(a) and f(b) are...
Is the statement true or not true? and why? "Every function where f(a) and f(b) are opposite in sign, there exists an x-intercept between x=a and x=b."
(5 pts each) Give example of an explicit function f in each of the following category...
(5 pts each) Give example of an explicit function f in each of the following category with properly written domain D and range R such that (a) There exists a subset S of D with f-'[F(S)] + S (b) There exists a subset T of R with f[f-(T)] #T (11) (3+3+ 5 + 5 + 2) Define functional completeness. Show that x + y = (x + y) + (x + y), x · y = (x + x) +...
Question 13 1 pts TRUE OR FALSE PRINGLE???? The point (-1, -1) is a saddle point...
Question 13 1 pts TRUE OR FALSE PRINGLE???? The point (-1, -1) is a saddle point for the function f(x, y) = x2 – 3y2 + 2(x – y). O True O False
(d) Given a function X Y show that each of the following statements are equivalent: (D) f is surjective (or, onto) (ii) there exists a function Y 4Xsucht hat.ro9주1r M for every pair of functions Y-ltLr/ifper Ctl
Incorrect Question 7 0/5 pts Which of the following proposition is true? (A) The clause {P(a,x,f(g(y))), P(z,f(z),f(u))} is unifiable and the set MGU = {[z/a], [x/f(a)], [u/g(y)]} is the most general unifier for it. (B) The clause (P(f(a),g(x)), P(7.7)} is not unifiable. (C) The clause {P(a,x), P(z,f(z))} is unifiable and the set MGU {[z/a], [x/f(a)]) is the most general unifier for it. (D) All of the above. (A (B) (C) (D)
The definition we gave for a function is a bit ambiguous. For example, what exactly is a "rule"? We can give a rigorous mathematical definition of a function. Most mathematicians don't use this on an everyday basis, but it is important to know that it exists and see it once in your life. Notice this is very closely related to the idea of the graph of a function. Definition 9. Let X and Y be sets. Let R-X × Y...
Question 13 5 pts Determine whether the function is one to one or not: {(-3,-5) (-2,-4) (-1, -3) (0, -2)(-1,-1) (-2, 0) (-3, 1)} Yes No, it is not one to one Oo oo Not a function None of the above. 5 pts Question 14 Find the inverse of the function: f (x) = x3 + 13 f'(x) = V2 - 13 y=2-13 33 = 2 - 13 None of the above. Question 15 5 pts Given f (x) =...
Question 13 4 pts Which of the following hydrocarbons has one pi bond and one cycloalkane? A) C6H8 B) C5Hg C) C3H8 D) C4H8 OB ОА Ос OD 4 pts
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Notice that the following claim is among one of the multiple steps of proving an important result: if A C and B D then A × B C × D. Claim: Let f : A → C and g : B → D be two surjective (onto) functions. Then h: A x B-> C D defined by ћ((a, b))-(f(a), g(b)) is a well-defined function that is surjective. Proof: Since f maps each a E A into f(a)...
A function f : A - B is said to be injective (or one-to-one) provided Va, a2 € A, f(a) = f(az) ► a1 = . A function g: A + B is said to be surjective (or onto) provided W6 € B, 3 some a € A such that g(a) = b. A function h: A → B is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective. The following...
(5 pts each) Give example of an explicit function f in each of the following category with properly written domain D and range R such that (a) There exists a subset S of D with f-'[F(S)] + S (b) There exists a subset T of R with f[f-(T)] #T (11) (3+3+ 5 + 5 + 2) Define functional completeness. Show that x + y = (x + y) + (x + y), x · y = (x + x) +...
Question 13 1 pts TRUE OR FALSE PRINGLE???? The point (-1, -1) is a saddle point for the function f(x, y) = x2 – 3y2 + 2(x – y). O True O False
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