Define reflexive closure and symmetric closure. Find the remainder when 4×2 – x + 3 is divided by x + 2 using remainder theorem.

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Define reflexive closure and symmetric closure. Find the remainder when 4&#215;2 &#8211; x + 3  is divided by x + 2 using remainder theorem.

Suresh Chand · Accepted Answer

Suppose, for example, R is not reflexive. If so, We could add missing ordered pairs to this relation to make it reflexive. Which is caused reflexive closure i.e. The reflexive closure of a relation R on set A is obtained by adding (a, a) to R to each a ∈ A. It is denoted by R ∪ △, where △ = {(a, a) : a ∈ A} Similarly, the symmetric closure of R is obtained by adding (b, a) to R for each (a, b) ∈ R. It is denoted by R ∪ R-1, R-1 = {(b, a) : to each a, b ∈ R} Problem Part: Let p(x) = 4x2 + x + 3 Putting x + 2 = 0 x = -2 Now, by remainder theorem Remainder = p)-2) = 4 (-2)2 + (-2) 3 = 16 + 1 = 17 ∴ By remainder theorem, the remainder when 4x2 - x + 3 is divided by x + 2 is 17

Define reflexive closure and symmetric closure. Find the remainder when 4x² – x + 3 is divided by x + 2 using remainder theorem.

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Define reflexive closure and symmetric closure. Find the remainder when 4x2 – x + 3 is divided by x + 2 using remainder theorem.

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Define reflexive closure and symmetric closure. Find the remainder when 4x² – x + 3 is divided by x + 2 using remainder theorem.