We partitioned the integers into three sets using x mod 3 (remainder is 0 1 or 2

Question

We partitioned the integers into three sets using x mod 3 (remainder is 0 1 or 2) : [0] = { … -9, -6, -3, 0 , 3 , 6 , 9 , 12, …. } [1] = { … -8, -5, -2, 1 , 4 , 7 , 10, 13, …. } [2] = { … -7, -4, -1, 2 , 5 , 8 , 11, 14, …. }

a. Is -154 in [0] or [1] or [2] Explain

b. Is 233 in [0] or [1] or [2] Explain

c. We saw that the difference integers selected from the set [0] or [1], [2] result in a multiple of 3 what about the sum of two integers from one of the sets [0] or [1], [2] ? Select a number from set [1] and another from set [2] is their sum in [0] or [1] or [2]

Explanation / Answer

in general, modulas is calculated as, dividend - quotient*divisor= remainder.

a. when we take -154mod 3 = 154/3=51.333. -154 - [51*(-3)]= -1 so mod 3 will be 3-1=2. hence -154 falls under [2].

b. 233 mod 3 = 233/3= 77.666. 233 - [77*3] = 2. 2 mod 3= 2. hence it comes under [2].

c. any no from [1] added with [2] results in integer value in set [0].

eg. - 5+ - 4= - 9, - 2 + - 1= -3, 1+2= 3 where -9, -3, 3 fall under [0].

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.