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Asked by rakeshwahengbam8 | 28 Dec, 2020, 11:52: AM
Q: Let R be a relation in R defined by (a, b) belongs to R iff 1 + ab > 0, for all a, b belongs to R. Show that R is reflexive and symmetric but not transitive.
Sol:
R is reflexive if (a, a) belongs to R for every a belong to R
Now, a2 > 0
Therefore, 1 + a2 > 0
Thus, (a, a) belongs to R.
Let (a, b) belongs to R.
Therefore, 1 + ab > 0
i.e. 1 + ba > 0
So, (b, a) belongs to R
Thus, R is symmetric.
Let (a, b), (b, c) belongs to R
Therefore, 1 + ab > 0 and 1 + bc > 0
But we can't conclude that 1+ac>0
So, R is not transitive.
Answered by Renu Varma | 06 Jan, 2021, 11:46: AM

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