sets F is (F,+,) a field? a) F - (a - bv2|a, bEZ} b) F- (a+ bV2[a, bEQ} c) F - (a + bV2+ cVA|a, b, cEQ}

Q: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

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Q: (p → (q ^ r)) ^ (1p → (1q ^ Tr))

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Q: What is the area of the kite? (2, 2) (-4, –2)(6, - 2) (2, - 6)

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Q: Show that if both f: A ---> B and g: B ----> C are bijective, then g 0 f: A ---> C is bijective.

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Q: Determine: 1 [1 -1 2]}-1 [2 3]+|0 1 -1

A: Step:-1 Given that  1-124-1023+1001-1-1Take U=1-124-1023+1001-1-1Since, we…

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

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Q: What is the output of the circuit corresponding to the Boolean expression (PAQ) V (~Q v R) when: P =…

A: See the detailed solution below.

Q: Find u, u = (-1, 4), v = (4, 5) (a) ||u|| v, uv, and d(u, v). (b) ||v|| (c) (d) U V d(u, v)

A: The given vectors u=-1, 4, v=4, 5. We have to find the values of u, v, u.v, du, v.

Q: Create 1 function for each of the following parts which has the following domain: a) [0, ∞)  b) (0,…

A: We have to Create one function for each of the given domain. “Since you have posted a question with…

Q: |고2 y 2리1- (y?-고2)(22 - 교2)(22 - y}) y 24 1. 1.

A: To show that

Q: t U=(-5,9) be universal and set A=(-3,4)  B=(-1,6) , D=(0,8) Find the following: (i)(AnB)' (ii)BuD'

A: We can solve this question with the help of number line: Given set  U=(-5,9) A=(-3,4) B=(-1,6) And…

Q: Find (a) * Find ux v, where: (a) u=(1,2,3), v=(4, 5, 6); (b) u=(-4,7,3), v = (6, —-5, 2). (a) [-3,…

A: To find the cross product of the given vectors.

Q: (12) 1. A (BC) . 2. (13) 1. ~ (CA)/:. ~B (A-B) v (C-D) 2. ~Al.. C (14) 1. Dv~ A 2. 3. ~(A.~B) ~ C…

A: Solution:

Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m ) + ( - n ) = - ( m + n)

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Q: Evaluate SA(u) du if A(u) a) 6i+8k b) -6i+8k c) 61-8k (3u²-1)i + (2u-3)j + (6u²-4u)k. d)-61-8k

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Q: Suppose that ab = ba, i.e., a and b commute. Determine |a^2 b^3 |, i.e., the order of a^2 b^3 .

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Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

A: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2.

Q: Evaluate: | 72³ · sec² (2³) dx = | Upload your handwritten work in the box below:

A: Use the method of substitution then integral by parts.

Q: (d) Find (AB)-' and (BA)-1.

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Q: ` Prove that positive real numbers a, b, c, d, b 2 + > 3.. a b+zc+3d +c+zd+za+d+za+36 d a+zh+30

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Q: Simplify the statement (p' v q)' v (p ^ (r v r')') v (p ^ q) using the laws of Boolean algebra.

A: Solution:Given         (p'∨q)'∨(p∧(r∨r')')∨(p∧q)To simply the statement using laws of Boolean…

Q: Find |AT|, |A²|, |AAŢ|, |2A\, and |A¯¹]. 4 03 A 2-1 5 1 46 (a) IATI (b) |A²| (c) JAATI

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Q: find (26-30)'3, BC 42A, CeTo)" BIC +2A, (CTD) カーク こZ) Glren A= -223 2-1 カー 5 こa 4 2

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Q: *218. 18 *$27+ 67 161 f

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Q: Question (2) 으 (2-3)" P(군)= Let then : %3D a Determine Zo=? and ana? b) Determine the Covergance…

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Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c 3 1(1-x*) ? +E E

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Q: f(x) 3* [(x+1) Sind 27x fx-2)

A: Givenf(x) = 3x27xexpress all the terms in 3 ( because 27=33) f(x) = 3x33x = 3x-3x= 3-2x = 132xTo…

Q: 1) (AUB) x C = (A x C)U (B x C) 2) ASBAXCSBXC 3) (Ax B) n (C x D) (AnC) x (Bn D)

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Q: @ 2 show Hhat fox) = e*-x3+2 2+2 is a %3D Permutation on R.

A: In the give question we have to show that the function f(x)=e-x-x3+2 is a permutation on ℝ.…