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Show that the relation R on the st A={ x...

Show that the relation R on the st `A={ xin Z:0lexle12}`, given by `R={a,b),|a-b|` is multiple of 4} is an equivalence relation.

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Show that the relation R on the set A={x in Z :0lt=xlt=12} , given by R={(a ,\ b):|a-b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1 i.e. equivalence class [1].

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Show that each of the relation R in the set A={x in Z :0lt=xlt=12} , given by(i) R = {(a , b) : |a - b| is a multiple of 4} (ii) R = {(a , b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.

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Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a – b| is divisible by 2} is an equivalence relation. Write all the equivalence classes of R .

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

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