Let R be the relation on the set of ordered pairs of positive integers such that
ID: 2981622 • Letter: L
Question
LetRbe the relation on the set of ordered pairs of positive integers such that ((a,b), (c,d)) is element ofRif and only if ad=bc.(1) show thatRis an equivalence relation (2) What is the equivalence class of (1,2), i.e., [(1,2)]? I know that for equivalence relations you need a binary relation that is reflexive, symmetric, and transitve. Do you put (a,b) (c,d) through these test or ad = bc....LetRbe the relation on the set of ordered pairs of positive integers such that ((a,b), (c,d)) is element ofRif and only if ad=bc.(1) show thatRis an equivalence relation (2) What is the equivalence class of (1,2), i.e., [(1,2)]? I know that for equivalence relations you need a binary relation that is reflexive, symmetric, and transitve. Do you put (a,b) (c,d) through these test or ad = bc....
LetRbe the relation on the set of ordered pairs of positive integers such that ((a,b), (c,d)) is element ofRif and only if ad=bc.(1) show thatRis an equivalence relation (2) What is the equivalence class of (1,2), i.e., [(1,2)]? I know that for equivalence relations you need a binary relation that is reflexive, symmetric, and transitve. Do you put (a,b) (c,d) through these test or ad = bc....
LetRbe the relation on the set of ordered pairs of positive integers such that ((a,b), (c,d)) is element ofRif and only if ad=bc.(1) show thatRis an equivalence relation (2) What is the equivalence class of (1,2), i.e., [(1,2)]? I know that for equivalence relations you need a binary relation that is reflexive, symmetric, and transitve. Do you put (a,b) (c,d) through these test or ad = bc....
LetRbe the relation on the set of ordered pairs of positive integers such that ((a,b), (c,d)) is element ofRif and only if ad=bc.(1) show thatRis an equivalence relation (2) What is the equivalence class of (1,2), i.e., [(1,2)]? I know that for equivalence relations you need a binary relation that is reflexive, symmetric, and transitve. Do you put (a,b) (c,d) through these test or ad = bc....
Explanation / Answer
YES YOU HAVE TO CHECK ALL FOR AD=BC...
1.REFLEXIVE ....TO CHECK IF ................
[A,B] R [A,B]..........WE HAVE AB=AB ..OK.....
2. SYMMETRIC .......TO CHECK IF [A,B] R [C,D[ ..THEN WHETHER [C,D] R [A,B] ......BOTH NEED SAME CONDITION AD=BC...OK....
3....TRANSITIVE ...GIVEN [A,B] R [C,D] ...AND....[C,D] R [E,F] ...IS [A,B] R [E,F] ??
AD=CB....CF=DE....IS AF=BE...
AD*CF=CB*DE...AF=BE......OK............
4. SO R IS EQUIVALENCE RELATION ......PROVED ...........
EQ.CLASS OF [1,2] ..WE SHALL HAVE ...
[1,2] R [P,Q] ......Q=2P....SO THE EQUIVALENCE CLASS IS [P,2P]......
WHERE P COULD BE ANY POSITIVE INTEGER
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