Relation Question need help
Let R be a relation on integers defined by (a,b) is a subset of R if a+3b is divisible by 4. Prove that R is and equivalence relation.
How to start this question can someone explain
How to start this question can someone explain
Original post by bigmindedone
Let R be a relation on integers defined by (a,b) is a subset of R if a+3b is divisible by 4. Prove that R is and equivalence relation.
How to start this question can someone explain
How to start this question can someone explain
Work through the three axioms of an equivalence relation.
For all x integer, is (x,x) a member of the subset?
Etc.
Original post by ghostwalker
Work through the three axioms of an equivalence relation.
For all x integer, is (x,x) a member of the subset?
Etc.
For all x integer, is (x,x) a member of the subset?
Etc.
i think i got through symetric and reflexive but for transitive i 4|a+3b and 4|b+3c then 4|3a+c i just wrote down those but i dont see how it proves it because what if in the cases like a even odd and stuff
Original post by bigmindedone
i think i got through symetric and reflexive but for transitive i 4|a+3b and 4|b+3c then 4|3a+c i just wrote down those but i dont see how it proves it because what if in the cases like a even odd and stuff
Should be 4|a+3c
If 4 divides the first two, try adding them together (a+3b) + (b+3c)
Original post by ghostwalker
Should be 4|a+3c
If 4 divides the first two, try adding them together (a+3b) + (b+3c)
If 4 divides the first two, try adding them together (a+3b) + (b+3c)
Ah i get it if 4 divides two numbers then it divides their sum
so 4| a+4b+3c thanks alot man
Original post by bigmindedone
Ah i get it if 4 divides two numbers then it divides their sum
so 4| a+4b+3c thanks alot man
so 4| a+4b+3c thanks alot man
Yep, and hence 4| a+3c, since 4|4b
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