CBSE Class 12-science Answered
confuse
Asked by rakeshwahengbam8 | 28 Dec, 2020, 11:52: AM
Expert Answer
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
Application Videos
Concept Videos
CBSE 12-science - Maths
Asked by saipranay8688 | 11 Aug, 2024, 16:19: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by niharika198two | 11 Jun, 2024, 11:36: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by srampratap206 | 17 May, 2024, 13:01: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by bornalimalakar3 | 05 Oct, 2023, 11:15: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by gdeadshot85 | 01 Apr, 2023, 12:15: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by rakeshwahengbam8 | 28 Dec, 2020, 11:52: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by darshansh200 | 28 Jul, 2020, 13:44: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by prakriti12oct | 06 Jul, 2019, 00:40: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by alanpeter9611 | 26 Feb, 2019, 02:14: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by niharikapabba2605 | 12 Oct, 2018, 12:43: PM
ANSWERED BY EXPERT