Transitive Sets Examples

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Let S be the set of all polynomials of degree at most 3. An element s of S can then be expressed as s=a x^3 b x^2 c x d, where a, b, c, d ∈𝐑. A relation R is defined on S by p R q if p and q have a root in common. (For example, p=(x-1)^2 and q=x^2-1 have the root 1 in common so that p R q.) Determine which of the properties reflexive, symmetric and transitive are possessed by R. | Numerade

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