Question

15. Given the relation R = {(1, 2), (2, 3)) on the set A = (1,2,3), add a minimum number of
ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.
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Answer 1

Answer:

Hence, the total number of ordered pairs is 7.

R is reflexive if it contains (1,1)(2,2)(3,3)

∵(1,2)∈R, (2,3)∈R

∴R is symmetric if (2,1),(3,2)∈R

Now, R={(1,1),(2,2),(3,3),(2,1),(3,2),(2,3),(1,2)}

R will be transitive if (3,1);(1,3)∈R. Thus, R becomes and  

equivalence relation by adding (1,1)(2,2)(3,3)(2,1)(3,2)(1,3)(1,2). Hence,  

the total number of ordered pairs is 7

Step-by-step explanation:

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Answer 2

Answer:

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