cse20_quiz_4_5

# cse20_quiz_4_5 - = 127 90 = 37 Quiz 5 Show that a(b.c =(a...

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Quiz 4 Given (m 1 , m 2 , m 3 ) = (2,5,9) , find x:(1,2,1) [note: x:(1,2,1) means (r 1 ,r 2 ,r 3 ) = (1,2,1) for the given (m1,m2,m3) ] Solution: Given, m 1 = 2 m 2 = 5, m 3 = 9, we have M = m 1 * m 2 * m 3 = 2*5*9 = 90 M 1 = m 2 *m 3 = 45 M 2 = m 1 *m 3 = 18 M 3 = m 1 *m 2 = 10 First, we find (S 1 , S 2 , S 3 ) so that (M i * S i ) % m i = 1 S1: (M 1 * S 1 ) % m 1 = 1 =>(45 * S 1 ) % 2 = 1 => S 1 = 1 S2: (M 2 * S 2 ) % m 2 = 1 =>(18 * S 2 )% 5 = 1 => S 2 = 2 S3: (M 3 * S 3 ) % m 3 = 1 =>( 10 * S 3 ) % 9 = 1 => S 3 = 1 =>(S 1 , S 2 , S 3 ) = (1,2,1) Following the Chinese remainder theorem, we have the formula x = ( M 1 S 1 r 1 + M 2 S 2 r 2 + M 3 S 3 r 3 ) % M = (45 *1 *1 + 18 * 2*2 + 10*1*1) %90 = (45 + 72 + 10) %90

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Unformatted text preview: = 127 % 90 = 37 Quiz 5 Show that a+(b.c) = (a+b).(a+c) [note: + denotes or operation, . denotes and operation] Proof by Truth Table: ID a b c b.c a+(b.c) (a+b) (a+c) (a+b). (a+c) 1 1 1 2 1 1 3 1 1 1 1 1 1 1 4 1 1 1 1 1 5 1 1 1 1 1 1 6 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 From the table, we can see that the columns for a+b.c and (a+b).(a+c) have same values of 0's and 1's. Therefore, a+(b.c) = (a+b)(a+c)....
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cse20_quiz_4_5 - = 127 90 = 37 Quiz 5 Show that a(b.c =(a...

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