(a1, a2) ∈R implies that (a2, a1) ∈ R, for all a1, a2∈A. This condition is for which of the following relations?a)Equivalence relationb)Reflexive relationc)Symmetric relationd)Universal relationCorrect answer is option 'C'. Can you explain this answer?

Question

(a1, a2) &isin;R implies that (a2, a1) &isin; R, for all a1, a2&isin;A. This condition is for which of the following relations?a)Equivalence relationb)Reflexive relationc)Symmetric relationd)Universal relationCorrect answer is option 'C'. Can you explain this answer?

Answer

It appears that you are referring to a tuple with two elements, a1 and a2. A tuple is an ordered collection of elements that can be of any data type. In this case, a1 and a2 could be variables, values, or objects.

Answer

The above is a condition for a symmetric relation.
For example, a relation R on set A = {1,2,3,4} is given by R={(a,b):a+b=3, a>0, b>0} 1+2 = 3, 1>0 and 2>0 which implies (1,2) ∈ R.
Similarly, 2+1 = 3, 2>0 and 1>0 which implies (2,1)∈R. Therefore both (1, 2) and (2, 1) are converse of each other and is a part of the relation. Hence, they are symmetric.

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