Question

Problem 1. (20) (a) Let a,b ? ?. Define a relation a ? b if 2 | a - b. Show that ? is an equivalence relation. (b) Use the relation defined in part (a). Let a,b,c,d ? ?. Suppose that a ? b (mod n) and c ? d (mod n). Prove that ac ? bd (mod n).

          Problem 1. (20) (a) Let a,b ? ?. Define a relation a ? b if 2 | a - b. Show that ? is an equivalence relation.
(b) Use the relation defined in part (a). Let a,b,c,d ? ?. Suppose that a ? b (mod n) and c ? d (mod n). Prove that ac ? bd (mod n).

Problem 1. (20) (a) Let a,b ? ?. Define a relation a ? b if 2 | a - b. Show that ? is an equivalence relation.
(b) Use the relation defined in part (a). Let a,b,c,d ? ?. Suppose that a ? b (mod n) and c ? d (mod n). Prove that ac ? bd (mod n).

Added by Luis W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/26/2023

Step 1

Reflexivity: For any integer a, 2 | a - a, so a = a (mod 2). Show more…

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Problem 1. (20) (a) Let a,b ∈ ℤ. Define a relation a ≡ b if 2 | a - b. Show that ≡ is an equivalence relation. (b) Use the relation defined in part (a). Let a,b,c,d ∈ ℤ. Suppose that a ≡ b (mod n) and c ≡ d (mod n). Prove that ac ≡ bd (mod n).