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Q: Prove: | a | - | b | <= | a + b |

A:

Q: Evaluate fc 713 where C : |z| = 2. Ans. fc z+1)3 Ti ( – 4). 1 z² (z+1)³

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Q: 4|\B Prove that (V3+ i)6 = -64

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Q: $50 and all m on these mov escribes this n buy

A: we have to write the inequality that describes the given situation  During a special sale all video…

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: 4+48 llv C44 23. 14c < 9c + 5 ++++ +++++ -4 -3-2-1 0 1 2 3 4

A: We have to solve

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: 20 2 Compute det B* where B = 113 2 2 2

A:

Q: discrete

A: Let a and b be the integers.It is given that if a|b or a divides b then a2 must divides b2 that  is…

Q: 5. Prove that arg(z1zz) = argzi – argzz %3D

A: Introduction: For a complex number z=x+iy, where x is the real part and y is the imaginary part,…

Q: 4) If FA1 AD, ED 1 AD, AB DC , and FC EB, prove FC EB.

A: Similar triangles

Q: 6. Compute 1,= de for p= 0,1 10

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Q: if U ={1 2 3 4 5 6 7 8 9 10} A={1 3 5 7 9} B={1 2 5} what is A'? what is B'? what is A'uB'?

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Q: 3- Compute (3-5*)(J5li +3). any leave your answer in sfandard fam

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Q: 4. Let A C BCR. Prove A° C B°.

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Q: 2.1. Prove that B Is erse of A -17 11] -7,B: 0 3 2 [1 1 2 2 4 -3 [3 6 -5] 2 A = -1 11

A: To prove that B is the inverse of A.

Q: 7. Prove: Vn,meZ, if n and m are odd, then n·m is odd.

A:

Q: The gcd (₁5,₁8) is: U15, U18 a) 2 b) 3 c) 5 d) 1

A: We need to find gcd(u15, u18): since U(15)={1,2,4,7,8,11,13,14} so order of U(15)=8 that is u15=8…

Q: A = 13 ;Prove A2 - 5A = 21

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Q: 2) Find VH if DH=1 U H G

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Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: If X ~N (6.7,25), then 1) u = ; 2) o² = ; o = 3) P(8<X<14) = .

A: Reviewing information, Given, X~N(6.7 , 25)

Q: II. Prove/Disprove: 1. (¬A → → ¬B) + (¬C A A) = ¬ (A V –¬B) + (В — С)

A: We will check whether the given statement is equivalent or not.

Q: jP a € Z then 24 4 is not afactor of 3 + |

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Q: 1 1 1 1) Show that с 3(6 -а)(с-а)(с-b) а a? b? c?

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Q: 4. Prove or provide a counter example for the following: (AU B)nC = (AnC)U(BnC)

A: We need to prove that(A∪B)∩C=(A∩C)∪(B∩C)If we have to prove that(AUB)∩ C C C…

Q: تفاضل وتكامل )2( نظري 1 If pconverges, then p could be xP to Select one: а. 3/2 stion 1 b. 1 Oc. non…

A: We have to check

Q: what is the iength of XY in ine figurebeiow 6) 12 c) 2J3 du3 sd el 6J 3 60

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Q: II. Prove the following. 3. 7|23n – 1, Vn EN -

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Q: 4 5 98 93 rnative hypothesis to test if the populatic ons differ from 0.20. portions are equal to…

A: the result for the provided data

Q: 3. Evaluate ". a, Inutc b. In u C. Inx+c

A:

Q: 3. prove that: det (AB) = det (A) det (B) If 2 -1 7 2 B = A 3 2 -3 4

A: In the question it is asked to prove the property det(AB)=det(A).det(B). Where A=2-132 and B=72-34

Q: w Write down the de finition of IT. 5.

A: Please go through the given definition of Pi given below,

Q: 4. Given that aj = 3, ) ak = 1 and ) bk = 5, it follows that k=1 k=1 Eak and > 2ak + bk k=2 k=1 8.…

A: Calculus   -  summation and  series

Q: 21 41 Verify the following directly if A = 1. B = |; .c = [, а. A(ВC) %3D (АB)C b. А(B+C) %3 AB + AC…

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Q: 7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

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Q: CW 17 - 3/9 Goriven: <I ☆c5 Prove: rfes Inot pavallel) 2.2 井23 (Indixect proob). %24

A: Given that, ∠1≢∠5 We have to prove that, r∦s.

Q: Show that  1/3 Tn + 2/3Mn ) = S2n.

A: By definition, Tn=12∆xfx0+2fx1+....+2fxn-1+fxnMn=∆xfx1+fx2+.....+fxn-1+fxn…

Q: 12.42. Let a, be Z, where not both a and b are 0. Prove that if d = gcd(a, b), a = ajd and b = b1d,…

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Q: (9.1) Suppose u = (-6, 6) and v = (-2, –1). Find a. Ju| b. [2u с. и-v d. Ju – v|

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Q: 5- Determine whether each of the following is singular or nonsingular: [3 2 41 A = 5 1 6 2 0 3] [1 2…

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Q: II. Prove/Disprove: 1. (¬A → ¬B) Ð (¬C ^ A) = ¬(A v ¬B) →¬(B –→ C)

A: Solve the Expression using boolean algebra   ¬a⇒¬b=a∨¬b(a∧¬c)⊕(¬a⇒¬b)=(a∧c)∨(¬a∧¬b) Also, the…

Q: 2 3 5 QIB) prove A.A1=I if A- 4 16 1 4 0

A: A detailed solution is given below

Q: Let 38c2 312 3 3104 S = 1+ 3°c + 2! 3! 4! If In S = 2187, then find c. 23 O 7 27 31 47 19

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Q: and other 1 ns. (i) 7/40 .16 A committ departmen. departmen committee (i) There (ii) It shc (iii)…

A: Given, 3 officers of the production department 4 officers of the purchase department  2 officers of…

Q: ieN 6. (a) Uto, i+ 1] = (b) N[0,i+1]= ieN ieN 7. (a) URx[i,i+1] = (b) ORXlii+1l=

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Q: 2. Expand the following: (i) apxi (ii) 7 (√ga') (iii) A Bi

A: To expand: (i.) aijxj (ii.) ∂∂xigai (iii.) AikBi

Q: 2 E AUB implies that 2 E A and 2 e B. Select one: O True False

A:

Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

A:

Q: 4, Suppose P(A) 2 0.8 and P(B) > 0.5. Prove P(AN B) > 0.3. Hint: You may use P(AUB)< 1.

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.