Provide counterexamples for If (A −B) ∩ (A −C) = ∅, then B ∩ C = ∅.

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: Determine: if S = {4t - t2, 5 + t3, 5 + 3t, -3t2 + 2t3} is a basic for P3

A:

Q: Let A = {1}, B = {2}, and C = {3}. (a) Explain why A x B B x A. (b) Explain why (A x B) × C # A × (B…

A: Cartesian product: The cartesian product of the sets A and B is defined as the set of all the…

Q: Which of the following is equivalent to (1-x)(1+x) - 3x (2-x)? A. 3x² - 6x +1 B. -3²-7x + 1 C.-4x² -…

A: Recall: (a+b)(a-b)=a2-b2

Q: (b) (-1)" (b)(-1)*+-

A:

Q: Let A = [-2  6]              [2   8] Find 3A.  3A =

A:

Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: Evaluate lim,→1 ( 고-교) 2 x-1 x² –1.

A: Given that,limx→ 11x-1-2x2-1

Q: -3v-2≥-2

A:

Q: Vx + x – x

A: We rationalize the numerator

Q: Evaluate: ,(3y – 8y* + 9y²)dy | -2

A: let I = ∫-223y6-8y4+9y2dywe know that ∫-aaf(t)dt = 2∫0af(t)dt

Q: iven ux*² = (1,-4,0), find lữ LƯ JAC

A:

Q: log (x*+3x +9) = 2

A:

Q: For x2 + Bx + C = (x + a) (x + b), which of the followingmust be true?(a) ab = B and a + b = C(b) a…

A:

Q: Which of the following is equivalent to (1-x)(1+x) -3x(2-x)  A. -4x2 - 6x + 1  B. 2x2 - 7x + 1 C.…

A: Given expression is (1-x)(1+x) - 3x(2-x)

Q: Find x, and x2- -52 28 -5 5 X2 40 X =

A:

Q: Let A = [0  2]              [5 -2] Find -4A.  -4A =

A:

Q: 9=a(0)2+b(+c 17-a(82+ b(8)+C 18=a(18)2 +b(18)+C

A: Solve the equation to find a,b,c

Q: 1. Find (A-1 B-1), If 0 -2 1 A = [] and B = [ [²4] 0

A:

Q: a (x + 4y) = ax + 4ay Select one: O True O False

A: Given here a function and asked to find whether it is true or false

Q: If z 2 = Rep, then write za+iß as Ae B

A:

Q: xdx Evaluate x2 + 2x + 1

A: The integral to be solved is . Since the integration is indefinite; a constant of integration is to…

Q: Given w= (-4, 12), s=(-6, -2), and r=(4, 11), %3D find 6r-(w+s). 6r-(w+s) =(| , O)

A: This is related to vector addition sub, and mul

Q: 2n"-3x+2=o frcove 846 8ub +ga3 t8=0

A:

Q: Let ā 47- 57 and b - 27 + 3j + 4k. Find - 2ā - 36.

A:

Q: Let z₁ = 7 - ni, 2₂=2 m+ 3 i, and Z3=4-7 i If 2 Z₁ + Z₂ + 2 z3 = 28+5 i,find m and n: m n=

A:

Q: 1 xp= V2x + 1

A: To find: The value of integral ∫0412x+1dx. Given that: The integral is ∫0412x+1dx. Formula used: The…

Q: (a + b) (a+b+c) = a² + 2ab + b² + ac + bc Select one: O True O False

A: Solution-

Q: If A %3D аx + За, and B %3D 5ax + 2а, — баz, find @AB- АВ

A: ANGLE BETWEEN TWO VECTOR