Solve the simultaneous congruences: x = 3 (mod 2) x = 5 (mod 7) (x = 11 (mod 13) The relation R in the set Z on integers given by R={(a,b): a b is divisible by 5} Is a. Reflexive b. Reflexive but not symmetric. c. Symmetric and Transitive. d. Equivalence relation. Which of the following relations is not an equivalence relation on the set of integers. a. x Ry iff xy is an even integer. b. x Ry iff x+y is an even integer. c. x R yiff x = y. d. x Ryiff x ≤y

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A: Given the set, A=2, 3, 5, 11, 12, 13 and the relation ∀a,b∈A, a R b↔a≡b mod 3

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