Consider the following statements:
1. Parallelism of lines is an equivalence relation.
2. x R y, if x is a father of y, is an equivalence relation.
Which of the statements given above is/are correct?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

A

Explanation

Statement 1: Let l, m, n are parallel line and R is a relation.
`therefore l||l`, then R is reflexive.
and l||m and m||l, the R is symmetric.
also l||m, m||n implies l||n, then R is transitive.
Hence, R is an equivalence relation.
Statement 2: x is father of y then x is not the father of x, so relation is not reflexive.
Also, x is father of y but y is not father of x, so it is not symmetric.
And x is father of y and y is father of z does not imply that x is father of z so, it is not transitive too. So, this is not an equivalence relation. so, only statement 1 is correct.