) Let S be the non-empty set containing all a for which f(x): = monotonic for all xe R. Find S. 4a-7 3 -r³+ (a − 3).x² + x + 5 is

Q: Find f ∘ g, g ∘ f, and g ∘ g. f(x) = x2,    g(x) = x − 1 a). f ∘ g ?     b). g ∘ f?     c). g ∘ g?

A: Given f(x) = x2,    g(x) = x − 1

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: (a) An (B − A) = Ø.

A: Given data:- The given equation,  A∩(B-A)=φ

Q: For the predicate P(x, y) ::= [x + 2 = y], choose all the pairs of x and y such that P(x, y) is…

A: Given query is to find the correct option for the expression.

Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

A:

Q: Define two relations R1 and R2 on set positive integers. R, = {(a,b)|a > b} and R2= {(a,b)|a? = b }.…

A: Composition of relation

Q: Give an example where A, B ⊆ X and |A| = |B| but |X ― A| ≠ |X ― B|.

A: This cannot be possible if we take X to be finite set so we have to think an example where X is…

Q: 2 > ]x – 4| X-1

A: Given,          2x-1≥x-4

Q: 2. For all sets X, Y and Z, determine whether each of the statement is true or false. If it is true,…

A: (a) False. We know that if a set A has cardinality n , then it's power set P(A) has cardinality 2n…

Q: Suppose x ∈ R. Let p(x): x² - 2x - 15 < 17 then the statement x is (valid or invalid)?

A:

Q: Let Q(x, y) be the statement "x + y = x - y." If the domain for both variables consists of all…

A:

Q: Define two relations R, and R2 on set positive integers. R1 = {(a,b) | a > b} and R2= {(a,b)| a² = b…

A: Given that two relations R1 and R2 on the set of positive integers.                    R1=(a,b) |…

Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a&lt;b means that a…

Q: Let u = (2, -2, 3), v = (1, -3, 4), and w=(3, 6, -4). Evaluate the following 1. ||3u-5v+w||…

A:

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: 3. Let V be the set of all ordered triple in R³, and F, the set of real numbers, where the…

A:

Q: Which of the following defines the domain of |4x-8<12? A) -8<x<-4 B)-4 <x < 8 C) -1<x< 5 D) 1<x<5

A: We can solve the inequality in order to get the solution.

Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: Let X be a set (P(X), Δ,∩) where P(X) is the power set of X, and Δ is the symmetric difference. It…

A: Unity: Let R, +, ∘ be a ring. If the semi-group R, ∘ has identity element then it is called as unity…

Q: Proof the following statement in detail: ". Let x ∈ R. Prove that if 3x4 + 1 ≤ x7 + x3, then x >…

A:

Q: | Let A = P({1,{1}}}, B = P({0,1}), and C = P({0,1}) where P(S) is the power set of S. Find the…

A: (1){{0},{0,1}}(2){ϕ,{1},{{1}},{1,{1}},{0},{0,1}}(3)ϕ(4) Refer to explanation part below.   If you…

Q: ) Determine whether f(x) = is even, odd, or neither. r2 + x +1

A: we have to determine whether the given function is even, odd or neither

Q: Let Pand Q be two predicates. Prove that 3x [ P(x) V Q(x) ] 3x P(x) V 3x Q(x)

A: Given ,P &amp; Q are predicatesTo prove :∃x P(x) V Q(x) ⇔∃x P(x)  V ∃x Q(x)

Q: Let f(a, b) = (a + b+2) + (2a + 4b + 6)x + (a +b+c)x² and set F = {f(a, b) : a, b € R}. What is the…

A: let  fa,b=a+b+2+2a+4b+6x+a+b+cx2 and set F=fa,b:a,b∈ℝ claim- to find the value of c if f1,0+f0,1∈F

Q: (Væ)(3y)(x² + y = 0) (3x)(Vy)(x2 + y = 0) (3æ)(3y)(x2 + y = 0)

A: