Types of Relations (Solved Problem)
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- เผยแพร่เมื่อ 25 ส.ค. 2024
- Discrete Mathematics: Types of Relations (Solved Problem)
Topics discussed:
1) Solved problem on relation types.
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Great thought!
Homework Answer:
NOT Transitive
For example,
(2, 1) and (1, 3) belongs to R, but (2, 3) does not belong to R
But what if we take (1,2) and (2,1) belongs to R. Is (1,1) belong to R??
@@karimabou6493 Yes, but note the "for every" part in the definition. Hence, one such example doesn't show that the relation is transitive, but one counterexample is sufficient to show that the relation is not transitive.
Okey i get it now. Thank u so much😊
Can you explain me why it is symmetric then? We should consider all real numbers right...
So we can also write 3+2 and 2+3 ..won't be it then non symmetric?
@@jayap8355 The "relation" discussed in this thread has been with reference to the given homework (focusing on the disjunctive proposition: x=1 OR y=1), so I'm not sure what the implication is by your premise involving addition (3+2, 2+3)
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The last relation {x,y| x=1 or y=1 } is NOT TRANSITIVE because
When we have a set A={1,2,3}
(1,2),(2,3),(3,1) in this not all the all the pairs include one hence there’ll be a case where y is not = 1 or x is not =1 ((2,3)).
the answer is :not transitive see why
if a=1 the answer will be transitive
(a,b)=(1,2) and (b,c)=(2,3) then (a,c)=(1,3)
but if b=2 the answer will be not transitive : (a,b)=(2,1) and (b,c)=(1,3) then (a,c)=(2,3) and it isn’t satisfied the condition of a=1 or b=1 . i hope it’s clear
H/W Answer ;
Relation is not transitive since (a,1) belongs to R and (1,b) belongs to R but (a,b) does not belong to R
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it is transitive. considering a=1, b=1 and c=2, then result will still be 1,2. x=1 or y=1 doesn't mean that both can not be equal to 1
It won't be transitive.
Let a=2, b=1, c=2
(a,b) = (2,1)
(b,c) = (1,2)
(a,c) = (2,2) doesn't have a 1 in it.
And you cannot consider both a and b as 1 because the condition says that only one of the elements can be 1
What if we take a as 1, b as 2 and c as 3
(a,b) = ( 1,2), (b,c) = (2,3) and (a,c) =( 1,3)
Making it transitive
I think the solution for a relation to be transitive in this case is conditional because when a is 1, it's transitive and when a is any other number but b is 1, it is not transitive.
Answer to H.W : R is Not Transitive. For Ex - a=2, b=1, c=2.
Ye to fir transitive ho gaya according to ur values
Hi, great video. Please cover equivalence relation and equivalence classes in the next episode.
thanks
In my class, we just end number theory...
Maybe I will review discrete using your videos lol.
ps. most i love is your c programming and data structure
Homework Answer: Not Transitive.
For being transitive, it's not sufficient that X or Y be 1, the union of ordered pairs (a,b) and (b,c) must implies in the ordered pair (a,c). However, it's possible to not reach this answer. For example:
a = 3
b = 1
c = 2
(a,b) ^ (b,c) ^ (a,c)
(3,1) ^ (1,2) ^ (3,2)
Although "b" fits the criteria (Y = 1), the ordered pair (a,c) isn't a implication of the union of the ordered pairs (a,b) and (b,c).
Of course if a=1, b=2 and c=1, the implication of the union of the same ordered pair would fit the criteria. However, it isn't the only possibility.
Therefore, "X=1 or Y=1" is not a Transitive relation.
Good job
Isn't relation b) an equivalence relation on the real numbers ?
Yes it is..
Hi @4:01 why did you take x and y as 0 for reflexive and symmetric and why did you take 1 and -1 for antisymmetric and transitive? If we take same 0 for antisymmetric and transitive they will be accepted right?
Coz relation should satisfy all values..
My answer to homework is not transitive. Why? ⬇️
For it to be transitive: (a,b) belongs to R AND (b,c) belongs to R implies (a,c) belongs to R and that is not true.
For example: (0,1) belongs to R AND (1,3) belongs to R but (0,3) doesn't belong to R.
how can you say (0,3) doesn't belong to R ?please tell me.i'm confused.
@@haiderkhan2518 remember a or b has to always be 1. I find it helpful to play with different numbers and then make sure all conditions are satisfied.
❤❤
Not transitive
ig it is transitive(homework problem)
x * y != 0
is it reflexive or not and why
💀
Not transitive
Not transitive
Not transitive
Not transitive
x * y != 0 is it reflexive or not, do you know that, please help me
@@JustScript99it is not reflexive coz it's only true for 0×0!