If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b = c (mod n) (b) b2 = c?(mod n) (c) ab %3D ac(mod п) (d) All the above. O d O c O a

Q: If x² + y² = 4, then 0-12/0 00 04-4 0- - O 1. 13. de =

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Q: Consider the sentence (3xP(x) ^ 3xQ(x)) 3x(P(x) ^ Q(x)). Which of the following is true? A. The…

A: Let P(x) : x is such that x ≡ 1 (mod 3)         Q(x) : x is such that x ≡ 2 (mod 6)    Then,…

Q: Show that x2 = Y mod p has

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Q: et x, y E Z. We have (x+y)³ = (x+y)² (x+y) = (x² +2xy+y?)(x+y) = (x³+3x?y+3xy² + y³) = x³ + y3 od 3.

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Q: How do I prove this:  Let d ∈ N and let a, b ∈ Z. Prove or give a counterexample: If a 6≡ 0 (mod d)…

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Q: What are the values of d so that 15(mod d ) = 3?      A. d = {4, 6, 12} B. d = {8, 12, 24} C. d =…

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Q: (a) 55 mod 7. (b) –101 div 3.

A: (a) 55 mod 7  As 55 = 7•7+6 So that  55 mod 7 = 6 mod 7

Q: 98! =... .(mod101) (а) 60 (b) 50 (c) 51 (d) None of these Select one: • d x

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Q: Suppose that a and b are integers such that a = 45 (mod 71) and b = 53 (mod 71). Find an integer c…

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Q: If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b3 c (тod n) (b) b2 =…

A: Given below the detailed solution

Q: What is the exact value of csc > O 2√5 3 IN O-2 14 (¹4) ²

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Q: Which a. 24 b. 56 of the following is true? 3(mod4) 4(mod5) c. 62 = 4(mod4) d. 58 3(mod5)

A: We want to find true option.

Q: If x1 mod 17 = 5 then %3D x mod 17 = 7 x mod 17 = 6 Ox mod 17 = 5

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Q: (c) Find integers p and q so that 17p + 45q = 1. Show your working steps. (d) Using the result in…

A: Given that 17p+45q=1 has no solution such that p and q are integers which means gcd of (17, 45) is 1…

Q: One of the foll owing is not true: Oa 0= 10 mod 5 b None Oc 14=2 mod 6 Od 20 =0 mod 5 Oe -24 mod 6

A: Here we use rules of modular operation.

Q: Which of the following is true? a. 24 = 3 (mod4) b. 56= 4(mod5) c. 62 = 4(mod4) d. 58 = 3 (mod5) Oa…

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Q: If x98 = 1(mod 97) then possible value of x is of (a) 97 (b) 194 (c) 90 (d) 291 (е) None of these O…

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Q: 1. Find all r €Z satisfying each of the following equations. (a) 3r = 2 (mod 7) (d) 9r = 3 (mod 5)…

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Q: 1. A+B (mod 173) 2. C-D (mod 432) 3. 23 x E (mod F) 4. G+5 (mod 7) АВМ 1А A B C E F G Hannah 7550…

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Q: Which of the following is TRUE? -52%3D0( mod 13) OA. -1=-13( mod 13) OB. 446=-278( mod 7) OC. 1=0 (…

A: Only (A) is true.  The detailed solution is as follows below:

Q: On their anniversary, Luna received a box containing x violet flowers. The number of these flowers…

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Q: If a = b (mod n) and b =c (mod n) then which of the following is false. a = c (mod n) a = c3(mod n)…

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Q: HA-[-2]. If = O A-¹ O A-¹ = O A-¹ = O A-¹, 24 = find A-¹. 3 = 6 -4] [4-2] 6 -5]

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Q: Informal Exercise 20. Observe that 4| 102. Show that to find Rem(n, 4), you just need to replace n e…

A: We need to find the remainder when n is divided by 4 .

Q: True or False?  −29≡5(mod 17)

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Q: #5. Suppose that a = 2 (mod 113), and b = 5 (mod 113) What is (a b + 56b + 155) mod 113?

A: given a≡2(mod113),b=5(mod113)a3≡23(mod113)a3b≡235(mod113)56b≡280(mod113)56b≡54(mod113)155≡15mod113)

Q: 3. Use congruences to prove the following: (a) 4"-1 is divisible by 3 for every natural number n.…

A: (a-b) is divisible by n.

Q: If(20.02)Ba) ane mod pocnt of sides oc, CA AA A ABC, them the eguntrom of AB is リ2メ-39-3-0 2 2メナ4=0…

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Q: Ti If a = b (mod n) and b =c (mod n) then which of the following is true. (a) a = c (mod n) (b) a2 =…

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Q: 34 2(mod 8) is congruent modulo, then the equation of the congruent (a= b+km) O A. 34 = 2*4+26 %3D O…

A: If a≡b(mod m) then the equation of the congruent is a=b+km , where k is constant.

Q: Hanb(mod n) and b c(mod n) then which of the following is trae. (a) anc (mod n) () 2=c(mod n) (c)…

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Q: If (ax + bx) = n and 7+1 E(ax – bx) - 2 Σ bk) , then ak 77+2 -1

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Q: Let a, n be positive integers. Knowing that 15a – 13n = 1, we deduce that the multiplicative inverse…

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Q: No. T (40) Given that a(AKPQ) a(AKLM) A. 8 8 C. 3√6 D then KL is B. 4√6 D. 2√6 M

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Q: QUESTION 5 Consider the linear combination 1 = 13(3) + 19(-2) then, a. The multiplicative inverse of…

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Q: QUESTION 2 Which is correct? 72+ 5 = 32 (mod 9) 74 = 164 (mod 10) 19× 27 = 7– 3 (mod 6) 24 – 27 = 5…

A: 72 + 5 = 49+5             = 54             = 9 (mod 9)             = 32 (mod 9) Hence 1 is true. 7 4…

Q: (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).

A: (d) For all integers a and b, if ab=7 mod 12, then either a =1 mod 12 or a =7 mod 12

Q: If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b = c (mod n) (b) b2 =…

A: We know that the property of congruence

Q: C 1 a b (b²+ c²) mod 2 = ?, a, b, c EN - {0}

A:

Statements and Logic

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