Question

Which of the following ordered pairs must be added to the above relation to form its symmetric closure?

None, it is already symmetric.
(1, 0) and (2, 0) only.
(1, 0).
(0, 1) and (0, 2).

Answer 1

Without the original set of ordered pairs in the relation, it's not possible to definitively answer which pairs need to be added for symmetric closure. The general concept requires that for each (a, b) in the relation, (b, a) must also be present to make it symmetric.

Step-by-step explanation:

To determine which ordered pairs must be added to the relation to form its symmetric closure, we need the original set of ordered pairs in the relation (which is not provided in the question). However, the concept of symmetric closure relates to the property that for every element (a, b) in the relation, there must also be an element (b, a) to make the relation symmetric. In general, if (a, b) is in the relation and (b, a) is not, to achieve symmetry, (b, a) must be added.

If the relation is symmetric, then no additional pairs need to be added. An example demonstrating symmetry using commutative property is A+B=B+A, where the sum of two numbers is the same irrespective of the order they are added (e.g., 2+3=5 and 3+2=5). This illustrates the general principle of symmetry. Without having the specific relation's ordered pairs, it's not possible to answer the question definitively, but an understanding of the concept can be applied once that information is known.

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