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The function f ,defined by f(x) = (x-1)/(3-x) , has the same set as domain and as

range.

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range.

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If (D,+,•) is an integral domain such that 1∈D , then D is a field.

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Not every polynomial that is irreducible over Q[x] is irreducible over Z[x] .

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If ( R ,*1,*2) is a ring, then ψ : R × R → R :ψ(r1,r2) = r1 *2 r1 is a binary operation.

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Every subring of a non-commutative ring is non-commutative.

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The characteristic of a field containing (50−1)elements is 50.

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{α1 ,α2 , ….,αn} is a set only if all the αis

follow a given rule.

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follow a given rule.

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If G = < x > is of order 25, then x^a generates G , where α is a factor of 25.

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If G is a group such that o(G) = 2m , where m∈N , then G has a subgroup of order m.

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If σ is an even permutation, then σ² = I .

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