8. Which of the following is a derived rule? • A→ BH (3x) A → (3x) B • (Vx) (A → B) + (3x)A → (3x) B In each case, a positive answer needs proof; a negative answer needs a precise argument in connection with a carefully built countermodel.

Q: •La Evaluate doc (1+√

A:

Q: In R show that 21 b) all × 11² + 20y|l² = 11x + y² ² + 1x-y₁² 2/ er

A:

Q: IEvaluate Ax)-2x+3x-4 A) x-3 B) x-h+/

A:

Q: Multiply: 3y2(2y³ - 4y² + 5y) a. 6y5-12y + 15y³ d. 5y5-y¹ + 8y³ b. 5y6-y4+8y² e. 6y5-y4+ 15y³ c. 6y6…

A: SOLUTION-

Q: What’s (E∩F)×(F∪G)

A: We are given that E = {1, 2}, F = {2, 3} and G = {3, 4}.Now, E∩F = {2} and F∪G = {2, 3, 4}.

Q: -2 7 -6 Let F= 4 4 | and G= 7 1 -1 2 - 4 2 Find – 6F+ 4G.

A:

Q: S(10) for √3 - 3 + 3√3+...

A:

Q: X1 Xi + 2x3 , X1, X2, x3 ER – 4.x2 T: R³ → R², T x2 X3 - x3 ||

A: So first we prove that the given transformation is linear

Q: Two students are having an argument. Remington says the cross product cannot be done in R° but…

A:

Q: Subtract-y2+8y from the difference between 9+ y² +6y3 and 5-y-5y³ Express the answer in standard…

A:

Q: (2+2x) e4+2² dæ her tonic

A:

Q: Q closed over multiplication? (Y/N) 6. Is N closed over multiplication? (Y/N)

A:

Q: ' EVALUATE (a) lem x² I メ→ 43×キ3x+1」 メナー* ×43x43x+1 (C) lem x2i 7ー ×+」

A: Given: (a) limx→-1- x2-1x3+3x2+3x+1(b) limx→-1+ x2-1x3+3x2+3x+1(c) limx→-1 x2-1x3+3x2+3x+1  To find:…