Let A = { - 4, - 3, - 2,01,3,4} and R = {(a,b) in A X A:b = |a| or b^{2} = a + 1} be a relation on A. Then the minimum number of elements, that must be added to the relation R so that it becomes reflexive and symmetric, is end{enumerate}: Relation (Mathematics)

Exam ($13^{th\ }$ April $2^{nd\ }$ Shift 2023)

Mathematics

Let

A = \{ - 4, - 3, - 2,01,3,4\}

and

R = \{(a,b) \in A \times

A:b = |a|

b^{2} = a + 1\}

be a relation on

A

. Then the minimum number of elements, that must be added to the relation

R

so that it becomes reflexive and symmetric, is

\

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Explanation

(7) : $R = \{( - 4,4),( - 3,3),(3, - 2),(0,1),(0,0),(1,1)$ , $(4,4),(3,3)\}\\$ For reflexive, number of elements added to the relation $R$ is $( - 2,2),( - 4, - 4),( - 3, - 3)\\$ For Symmetric, number of elements added to the relation is $(4, - 4),(3, - 3),( - 2,3),(1,0)\\$ So, total number of elements $= 3 + 4 = 7$

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Explanation

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