If $A$ be the set of all real numbers and R be the relation on A defined by $R = \{(a,b): a^2+b^2=1, \forall a,b \in A\}$, then R is

The relation R on the set of real numbers defined by $R = \{(a, b): a \leq b^2\}$ is

(A) Reflexive

(B) Not symmetric

(C) Neither reflexive nor transitive

(D) Transitive

Choose the correct answer from the options given below:

For the relation $R = \{(a, b): a \leq b\}$ in $\mathbb{R}$, which of the following is correct?

If R and S are two equivalence relations on a set A, then

Which of the following statements are true?

(A) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = 3x$ is one-one onto.

(B) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = x^4$ is one-one and onto.

(C) $f:\mathbb{Z} \to \mathbb{Z}$ given by $f(x) = x^2$ is neither one-one nor onto.

(D) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = |x|$ is neither one-one nor onto.

(Where $\mathbb{R}$ is the set of all real numbers and $\mathbb{Z}$ is the set of all integers)

Choose the correct answer from the options given below:

A relation R on the set $A = \{1, 2, 3, \ldots, 13, 14\}$ defined as $R = \{(x,y): 3x - y = 0\}$ is

Let $R : \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers and R be a relation. An element $(x, y) \in R$ if $x + y - \sqrt{2}$ belongs to the set of irrational numbers. Then the relation R is :