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Asked by jiyag9397 | 22nd Aug, 2020, 05:14: PM

Expert Answer:

A={1, 2, 3, ..., 13, 14}, R={(x, y):3x-y=0}
straight i.
For space open parentheses straight a comma space straight a close parentheses element of straight R comma space 3 straight a minus straight a equals 2 straight a equals 0 space only space for space straight a equals 0 space and space for space straight a not equal to 0 comma space 3 straight a minus straight a not equal to 0
So comma space open parentheses straight a comma space straight a close parentheses not an element of straight R space for all straight a element of straight A
Thus comma space straight R space is space not space reflexive
ii.
Let space open parentheses straight a comma space straight b close parentheses element of straight R space rightwards double arrow space 3 straight a minus straight b equals 0
left parenthesis straight b comma space straight a right parenthesis element of straight R space if space 3 straight b minus straight a equals 0 space
Now comma space 3 straight a minus straight b equals 0 space and space 3 straight b minus straight a equals 0 space are space true space only space for space straight a equals 0 space and space straight b equals 0
Therefore comma space open parentheses straight a comma space straight b close parentheses element of straight R space rightwards double arrow left parenthesis straight b comma space straight a right parenthesis element of straight R space does space not space hold space for all space straight a comma space straight b element of straight A
Thus comma space straight R space is space not space symmetric
iii.
Let space left parenthesis straight a comma space straight b right parenthesis comma left parenthesis straight b comma space straight c right parenthesis element of straight R rightwards double arrow 3 straight a minus straight b equals 0 space and space 3 straight b minus straight c equals 0
Consider space 3 straight a minus straight c equals straight b minus 3 straight b equals negative 2 straight b not equal to 0 space for space straight b not equal to 0
So comma space left parenthesis straight a comma space straight b right parenthesis comma space left parenthesis straight b comma space straight c right parenthesis element of straight R space does space not space imply space left parenthesis straight a comma space straight c right parenthesis element of straight R
Thus comma space straight R space is space not space transitive.

Answered by Renu Varma | 25th Aug, 2020, 10:50: AM