Show that if AB BA, then eA+BeAe, but if they do commute, then the relations hold. Hint: Write out several terms for e4+B, e4, e and do the multiplication carefully

Q: a – b -| < 1, if|a| < 1, and |b| < 1. 1- āb - Show that|-

A: From the given information. For , then show that .

Q: Show that if ac|bc, then a|b.Show that if a|b and b|a then a=±b.

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Q: Determine which of the following biconditional statements are true. (a) x² = 4 (b) lx-5 |<0 if and…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: = { (; ):a,b e R}with the standard operations in M22. Which of the following statements is true?

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Q: Prove the statement; a – c is a divisor of ab + cd=→a – c is a divisor of ad + bc.

A: We need to prove the statement; a – c is a divisor of ab + cd =&gt; a – c is a divisor of ad + bc.

Q: Determine if in the following diagram AADB is congruent to ACDB. D A They are congruent. O They are…

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Q: Let -2 0 A= -3 1 Find A-, if it exists. 1 2 а) 3 1 2

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Q: The symmetric property of congruence can be used to state that if 2SAT ZRUN, then ZRUN E ZSAT. True…

A: topic - symmetric property of congruence Symmetric property of congruence states that if shape 1 is…

Q: If for AMOP and ALUV, the correspondence AMOPALUV gives a congruence, then which of the following is…

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Q: Prove the following statement: a If A = b and ad - bc + 0, 1 d -b then A ad – bel-c a

A: we have to prove the following statement: if A=abcd and ad-bc≠0 then A-1=1ad-bcd-b-ca

Q: If a = qb +r, then gcd(a, b) = gcd(a,r).

A: In this question, we have to use the division properties with  a=qb+r to check GCD(a,b)=GDC(a,r)

Q: (a-b)’ (b-c)' P (-9) a 3 d

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Q: Prove the following statement: 2" ≥ 2n

A: We have to prove the following statement- 2n≥2n We will prove it using mathematical induction.

Q: Z Let AABC and ADEF have corresponding pairs of sides which are parallel. Say, AB || DE,BC || EF, AC…

A: given triangles are    △ABC  and   △DEF Also,       AB||DE,   BC||EF,   AC||DF yes it follows that…

Q: Let = {a,b}. Prove the equivalence: b + ε*bab((ab)*)* = b(ab)*.

A: We are going to prove that L.H.S = R.H.S

Q: Justify each statement with a property from algebra or a property of congruence. 5. If m&lt;A +…

A: 5- Given-  If m∠A+m∠B+m∠C=180° and m∠C=50°    m∠A+m∠B+50°=180° To justify- The above statement with…

Q: Tori was asked to give an example of the commutative property ofaddition. Which of the following…

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Q: Let P, Q and R be statements. Use substitution method by applying the laws given in Unit I…

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Q: ssume that the X1 and X2 are binary variables. What would be the appro onstraint expression if X1…

A: Topic:- probability

Q: Suppose R1 and R2 are relations on A. If R1 and R2 are both symmetric, then R1 n R2 is symmetric. O…

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Q: Which statement is an example of a transitive relationship? If x = 2y and 2y = 8, then x = 4. If clm…

A: Transitive relationship is a relationship in which if from the first two condition 3rd condition can…

Q: Show that ∗ : R × R → R given by         (a, b) → a + 4b2 is a binary operation.

A: Given for all real number a and b

Q: If the pth, qth and rth terms of an A.P. are a, b and c respectively, prove that : a(q – r) + b(r –…

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Q: The transitive property of congruence states that if 2 A = ZB and z B C, then A C. O True O False

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Q: Show that the operation * on Q – {1}, defined by a * b = a + b – ab for all a, beQ- {1} satisfies…

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Q: 1. Write the Final Colu statement. Write T for

A: Given logical statement is  (p∧~q)→(p∨q)

Q: If 3 1 0 A = | 5 2 -1 1 4 - 2 The adjoint of A is -1 1 9 9. 18 - 6 3 -11 – 11 1 True False

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Q: Suppose R1 and R2 are relations on A. If R1 and R2 are both reflexive, then R1 N R2 is reflexive. O…

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Q: Let jEZ (a) Prove directly the statement : If 3j, then 3j²

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Determine whether the here given statement is true or false. If the statement is false, make the…

A: Given : 712·712 = 49

Q: Write a congruence statement for the following diagram R

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Q: If a = qb +r. then gcd(a, b) = gcd(a,r).

A: In this question, we have to check the gdc(a,b)=gdc(a,r) if a=qb+r

Q: Prove the following statement: 2" ≥2n

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Q: Describe and correct the error in writing a similarity statement. 15 B 86 18 24 86 20 AABC APQR by…

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Q: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2 Show that a + b> c.

A: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2To Show:-  a + b&gt; c.

Q: Prove: If a &gt; b, then a &gt; 1/2 ( a + b ) &gt; b.

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Q: Identify the axiom or postulate that applies to the following statement.     If  x = AB + CD + EF +…

A: We have used the axioms here......

Q: Determine whether the statement, given in inverted commas" is trueor false. If the statement is…

A: we have to determine whether the given statement is true or false. Statement: "5 + 3(x - 4) = 8(x -…

Q: Which of the following relations complete the statement: If PQ = RS , then 'using the symmetric…

A: To fill in the blanks.

Q: Use the given information to provide a direct proof of the statement below. Prove that the product…

A: Product of two odd numbers is an odd number .

Q: Let S= {1, 2, 3, Question 5. 4} and G = S,. Write all of the elements of GT and G(T) in each case.…

A: Given, S={1, 2, 3, 4} and G=S4 We have to write all the elements of GT and G(T) in each case. (a) T…

Q: Example: Find dat(A) if 3 A = |-1 1 3 -6 4

A: Determinant of a Matrix: Let be the set of square matrices of order n. Then be a map defined by…

Q: It is known that P(A) = 0.7, P(B) = 0.4 and P(A and B) = 0.24. Which of the following is true?…

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Q: Let z, =1-1, z, =-2+4/, and z, = 3-21. Find Im().

A: Multiply z1 and z2 then divide by z3 then solve and get imaginary part

Q: 21. Suppose that A = B, = a1 +2a2, B, = (a) Prove that B (b) Find the follow (c) Find the trans

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Q: prove that if a>4 then (a-2)^2>4

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Q: all combinations of → r)) is true. (Highlig

A: p q r ~p p→r ~p→r q∧~p→r ~p↔q∧~p→r  T T  T   F T  F  F  T  T T F F F T T F T F T F T F F T F…

Q: 3u -w

A: