The discussion revolves around equivalence relations in mathematics, specifically focusing on the properties of transitivity and symmetry as they relate to the equation a/b = c/d. Participants are exploring the definitions and implications of these properties within the context of equivalence relations.
Some participants are providing guidance on the definitions of the properties of equivalence relations, while others are questioning the original poster's understanding of symmetry and transitivity. There is an ongoing exploration of how these properties apply to specific examples, and clarification is being sought regarding the nature of equivalence classes.
Participants are discussing the requirement for properties to hold for all pairs of values rather than individual values, which has led to some confusion. The original poster's understanding of the equivalence relation is being challenged, particularly regarding the conditions for symmetry.
Note that in the problem statement it says ##ad = bc \Leftrightarrow \frac a b = \frac c d##. IOW, these two equations are equivalent. You should not have the 2nd and 4th "equals" there.Kingyou123 said:
You're missing the point. R would be symmetric if (a, b) R (c, d) implies that (c, d) R (a, b).Kingyou123 said:
Kingyou123 said:
Symmetric= if (a,b)R(C,d) then (c,d)R(a,b) since ad=bcTeethWhitener said:
Nope, all pairs of values.Kingyou123 said:
Could you explain part b?TeethWhitener said:
For example 1/2 = 2/4 = 3/6, so (1,2)R(2,4) and (2,4)R(3,6). These three pairs are all equivalent and build together an equivalent class. One of them represents this class. But there are more classes.Kingyou123 said: