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1. Consider the following statement about three sets A, B and C: If An (BUC) = 0, then An B = 0 and AnC=0. Formulate both the contrapositive and the converse of this statement and decide whether each is true, giving reasons. From your conclu- sions, decide whether the original statement is true. 2. The greatest common divisor two integers n 0 and m #0 is the largest natural number d that divides n and m. It is denoted by ged(n, m). Prove that if d = gcd(m, n), then ged(, ) = 1.

1. Consider the following statement about three sets A, B and C: If An (BUC) = 0, then An B = 0 and AnC=0. Formulate both the contrapositive and the converse of this statement and decide whether each is true, giving reasons. From your conclu- sions, decide whether the original statement is true. 2. The greatest common divisor two integers n 0 and m #0 is the largest natural number d that divides n and m. It is denoted by ged(n, m). Prove that if d = gcd(m, n), then ged(, ) = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the following statement about three sets A, B and C: If An (BUC) = 0, then AnB = 0 and AnC = 0. Formulate both the contrapositive and the converse of this statement and decide whether each is true, giving reasons. From your conclu- sions, decide whether the original statement is true. 2. The greatest common divisor two integers n 0 and m #0 is the largest natural number d that divides n and m. It is denoted by ged(n, m). Prove that if d = gcd(m, n), then ged(77, 7) = 1.
Transcribed Image Text:1. Consider the following statement about three sets A, B and C: If An (BUC) = 0, then AnB = 0 and AnC = 0. Formulate both the contrapositive and the converse of this statement and decide whether each is true, giving reasons. From your conclu- sions, decide whether the original statement is true. 2. The greatest common divisor two integers n 0 and m #0 is the largest natural number d that divides n and m. It is denoted by ged(n, m). Prove that if d = gcd(m, n), then ged(77, 7) = 1.
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