n=23 satisfies one of the following congruence 24 + 27 =5+2 (mod n) O. 24 x 27 =5 (mod n) 24 + 27 =5 (mod n) 24 - 27 =5 (mod n)

Q: The statement a ≡ b (mod n) is called a congruence.

A: Given that  The statement a ≡ b (mod n) is called a congruence.

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A: To explain why Christmas and new year's day always fall on the same day of the week.

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 use the properties of congruences to answer the given question.

Q: 2. If a = 1 (mod p), then a=1 (mod p). Select one: True False

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Q: True or False : a – c ≡ b – c (mod n) ⟺ a ≡ b (mod n)

A: We have to solve given problem:

Q: If a =b (mod m) and a = b (mod n) then a = b (mod m+n) Select one: O True O False

A:

Q: If a ≡ b (mod n1) and a ≡ b (mod n2), must it be true that a ≡ b (mod n1 + n2)? Either give a proof…

A:

Q: n=23 satisfies one of the following congruence 24 - 27 = 5 (mod n) 24 x 27 = 5 (mod n) 24 + 27 = 5+…

A:

Q: 2221 (mod 13) is equal to O 10 (mod 13) O 1 (mod 13) 7 (mod 13) 6 (mod 13) O None of these

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Q: Which expression is equivalent to [77 · (-65) + 147] mod 7? O 7 O [(147 mod 7) · (-65 mod 7) + (77…

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Q: If x = 2 (mod 5) and y = 4 (mod 5) then 2x – 3y =? (mod 5)

A:

Q: If a ≡ b (mod n1) and a ≡ b (mod n2), must it be true that a ≡ b (mod n1n2)? What if gcd(n1, n2) =…

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Q: Solve each of the following congruences: (a) x = 6 (mod 10); x = 11 (mod 15) (b) x = 3 (mod 21); x =…

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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)…

A:

Q: Consider the congruence 9x   21 (mod 33). (a) Does 9 -1(mod 33) exist? Explain why or why not.

A:

Q: Which of the following are true modulo 12? (1) Does 5z = 6 mod 12 have a solution? How many? (2)…

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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 n is an integer, then (2n² + 3n)# 3(mod5).

A:

Q: 1 Solve the following system of congruences X= 2 (mod 3) x = 3 (mod 5) X= 2 (mod 7)

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Q: The equation 15x=30 (mod 50) has: 5 non-congruent solutions modulo 50 6 non-congruent solutions…

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Q: If 19 =7 (mod 6) and 27 =3 (mod 6) then 19x 27 = 7+3 (mod 6) 19+27 = 7+3 (mod 6) 19+27 =7x 3 (mod 6)…

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Q: Does 5x = 6 mod 12 have a solution? How many?

A: As per our guidelines we are supposed to answer only One question  if there are multiple questions…

Q: Which of the following satisfies the congruence 3x O O 2 T - 2 (mod 5)?

A:

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

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Q: Show that: if a = b(mod n) and C = d\modn), then a +c =b+d\mod n)!

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Q: Let a₁ = a₁ = a₂ = 2 and an = an-1 + an-2 + an-3 for n > 3. Prove, using strong ao mathematical…

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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

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Statements and Logic

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