Let +, is an operation defined on Z, = {0,1,2} as %3D 1 1 1 2 1 Then, identify the true statement from the following: إخفر أحد الخيارات Z, is not close with +,. a O None of these The operation +, is commutative on Z,. 1 is the identity element of the operation +, on Z, .cO The operation +, is not associative on Z,. e O 2) 2.

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

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Q: Find the devivative of f cx) = by Hhe de filzifion.

A: Here we differentiate the given function by it's definition.

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Q: Let is an operation defined on R by a*b=a+b-4, Va,beR. What is the identity element of the operation…

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Q: Simplify the following Boolean expression: Ax [A + (A' x B)] by using the laws of Boolean algebra

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Q: Define two operations + and * on A = Z × Z as follows: for (a, b) and (c, d) in A: ɔy (a, b)+(c, d)…

A: As per guidelines, we will solve first three subparts: Define two operations + and * on A=ℤ×ℤ as…

Q: Define a * b = 3a + b, where a, b € R. Find the following: 1. 8 * 3 2. 3 * 8 1+2 3. 3+4

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Q: Can you find a,b,c, and d (if exists) such that AB = BA.

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Q: Determine the multiplicative inverse of 11 in Z24. Your final answer should be an element of {0, 1,…

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Q: 1 0 7 -2 -2 2 land B =| 4 12 6 5 9 -2 evaluate -2A+B.

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Q: Evaluate the following * 5 Sa 4x - 1 In(4x - 1) 4 O II -dx + C 5ln(4x - 1) 4 + C 5ln(4x − 1) + C 4…

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Q: Show that [-a, b] is the additive inverse of [a, b] in Q.

A: To Prove -a,b is the additive inverse of a,b in ℚ. By definition of additive inverse, For y in ℝ,…

Q: Define the binary operator* by: a+b = a +8b and V by: aVb=6 Find the following. When simplifying,…

A: Given operators: a * b = a + 8b   .......(1)  a ∇ b = 6    .......(2)

Q: efine the binary operator @ by:      aa@b=2bb=2b and □□ by:      a□b=a2+b2a□b=a2+b2

A: Introduction: A operation could be an operation f (x, y) that's applied to 2 members of constant set…

Q: 6. b. a. does not exist Find the inverse of -1 -1 Ed -4 نما 3 -4 -1 1 if it exists. C. 1 1 B 4 3 d.…

A: Given that the matrix 3-1-41

Q: √38 10 V √ 65

A: To check whether the given triangle is right triangle or not.

Q: is called the multiplicative identity. • 0 -1 • 9 • 1

A: The multiplicative identity is 1because multiplying a number by 1 leaves it unchanged . If a is any…

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A: Consider Tn={n, n2}, where n is an integer. The objective is to find the number of elements in each…

Q: 4 Write the allIV Algebraic Identities with complete explanation.

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Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

Q: Use (9.11) and (9.12) to simplify (ABTC)T, (С-1мс) -1, (АН) -"(АНА-1)"(НА-1) -1.

A: For (ABTC)T by using (9.11) we get (ABTC)T = CT(BT)TAT As (BT)T = B Hence (ABTC)T = CTBAT

Q: 1 0 1 A = 1 1 0 0 1 1 0 1 1 B = 1 01 1 0 1

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Q: Suppose a is divisible by b. Show that gcd(a, b) = b.

A: Consider the given information. As we have given that a is divisible by b. then there is a number c…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.