Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B ?
{(1, 2), (2, 3), (3, 4), (2, 2)}
{(1, 2),(2, 3), (1, 3)}
{(1, 3), (2, 3), (3, 3)}
{(1, 1), (2, 3), (3, 4)}
Given,
[f(x)]3
- f(x)
3f(x)
None of these
Which of the following proposition is a tautology?
If N denote the set of all natural numbers and R be the relation on N
symmetric only
reflexive only
transitive only
an equivalence relation
D.
an equivalence relation
For (a, b), (c, d)
(a, b) R (c, d)
Reflexive: Since, ab(b + a) = ba(a + b), ∀ ab ∈ N
So, R is reflexive.
Symmetric: For (a, b), (c, d)
Let (a, b) R (c, d)
So, R is symmetric.
Transitive: For(a, b), (c, d), (e, f) ∈ N
Let (a, b) R (c, d), (c, d) R (e, f)
On multiplying Eq. (i) by ef and Eq. (ii) by ab, then we get
adbef + adcef + cfdab + cfeab
= bcaef + bcdef + decab + defab
So, R is transitive.
Hence R is an equivalence relation.