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Let A = - 4 , - 3 , - 2 , 0 , 1 , 3 , 4 and R = ( a , b ) ∈ A × 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

Correct answer

7

Step-by-step solution

Given, A = - 4 , - 3 , - 2 , 0 , 1 , 3 , 4 and R = ( a , b ) ∈ A × A : b = | a | or b 2 = a + 1 be a relation on A , So, the relation is given by, R = ( - 4 , 4 ) , ( - 3 , 3 ) , ( 0 , 0 ) , ( 1 , 1 ) , ( 3 , 3 ) , ( 4 , 4 ) , ( 0 , 1 ) , ( 3 , - 2 ) Now, relation to be reflexive ( a , a ) ∈ R   ∀   a ∈ A ⇒ ( - 4 , - 4 ) , ( - 3 , - 3 ) , ( - 2 , - 2 ) also should be added in R . Now relation to be symmetric if ( a , b ) ∈ R , then ( b , a ) ∈ R   &#8704

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