1. Determine whether the following relations are reflexive, symmetric or transitive :
- R on Z defined by (a, b)
R
|a-b|
5.
- R on Q - {0} defined by (a, b)
R
ab = 4.
2. If R is a relation in N*N defined by (a, b) R (c, d) if and only if a+d = b+c, show that R is an equivalence relation.
3. Let N denote the set of all natural numbers and R be the relation on N*N defined by (a, b) R (c, d)
ad(b+c) = bc(a+d). Show that R is an equivalence relation on N*N.
4. If
and
are two equivalence relation on a set A, then prove that
is also an equivalence relation on A.
5. Show that the number of equivalence relations on the set {1,2,3} containing (1,2) and (2,1) is two.
- R on Z defined by (a, b)
R
|a-b|
5.
- R on Q - {0} defined by (a, b)
R
ab = 4.
2. If R is a relation in N*N defined by (a, b) R (c, d) if and only if a+d = b+c, show that R is an equivalence relation.
3. Let N denote the set of all natural numbers and R be the relation on N*N defined by (a, b) R (c, d)ad(b+c) = bc(a+d). Show that R is an equivalence relation on N*N.
4. If and
are two equivalence relation on a set A, then prove that
is also an equivalence relation on A.
5. Show that the number of equivalence relations on the set {1,2,3} containing (1,2) and (2,1) is two.
Asked by abhinavsaini123
| 29th May, 2015,
12:56: PM
Please ask one query in a single post. The explanation for the first question is given below:


Answered by satyajit samal
| 30th May, 2015,
11:15: PM
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