Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Show that E∩F = {0} and f(E∩F) = {0}, while f(E) = f(F) = {y∊R : 0≤y≤1}. Hence f(E∩F) is a proper subset of f(E) ∩ f(F). What happens if 0 is deleted from the sets E and F?

Q: Prove that P(XY) = P(X)n P(Y) for all sets X and Y.

A:

Q: Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y):…

A: Given W(x): ' x is a woman' M(y):' y is a man'

Q: 2. Let X1 and X2 be sets. Define functions T1 : X1 × X2 → X1, T2 : X1 × X2 → X2 by T| (X1, X2) = x1,…

A:

Q: Suppose UCC is a domain, f, g = O(U). If |ƒ(z)|2 + |g(z)|² = 1 for all ZEU, show that ƒ and g are…

A: The solution to the problem is in the segment below.Explanation:To show that f(z) and g(z) are…

Q: Function f: {a,b)³ → (a,b) is defined by the following rule. For strings € (a,b)³, f(s) = f(x1x2x3)…

A:

Q: Show that the function f: [1, 2] → [1,8], f(x) = 7x - 6 is a bijection. What relationship exists…

A:

Q: Let W = (0, 1, 3}, X = {1, 3, 5), Y = (3, 4} and Z = {(1, 2), (3, 4), (1, 3),(2, 4). Compute (X x Y)…

A: The given problem is to find the Cartesian product of given sets and verify the Cartesian product…

Q: Consider f = {(x, y) : x ∈ N and x + y = 5}. Write out some elements of f. What are the domain and…

A: Given: f={(x,y): x∈N and x+y=5} The domain of a function f(x) is the set of all values for which the…

Q: Let C = {x ∈ P(A) : ∃y ∈ x, y ∈ A and y /∈ B}. Prove that P(A) − P(B) = C.

A:

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

A: Given that  where G,u and v are differentialblle functions

Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…

A:

Q: Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

Q: Let A = Z and B = Z. Suppose f: A ∈ B is defined by the rule f(a) = a3 + a + 1. Determine f(−1) and…

A:

Q: Let X be the set {5, –6, 2}. For the first three parts of this problem you are asked to define a…

A: Consider the set 5,-6,2. The function is f:X→X and the relation is u~w⇔w=fu.   a) The relation is…

Q: Select the following functions that are bijective. ƒ₂: R → R, ƒ₂(x) = 14 f₂: R → R, f₂(x) = x f₁: R…

A:

Q: For a derived varaible f : states → R is strictly decreasing if and only if for states q, q': → f(d)…

A: